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The generalized nonlinear Schrödinger equation with anti-cubic and cubic-quintic-septic nonlinearities is considered. A series of direct transformations is performed for the traveling wave reduction of the original equation. The implicit function method is used for nonlinear ordinary differential equation with some constraints on the parameters. Some analytical solutions are found in the form of periodic and solitary waves. Three conservation laws, corresponding to the generalized nonlinear Schrödinger equation are obtained and conserved quantities corresponding to the solution in implicit form are found [ABSTRACT FROM AUTHOR]

The optical solitons represent a fascinating intersection of nonlinear physics and optical technology. In this study, we examine the three-component Dirac–Manakov system through the application of a unified Darboux transformation. We elaborate on the construction of the n-fold Darboux transformation and elucidate the correlation between optical solitons and seed solutions. Our research successfully yields both single-soliton and double-soliton solutions derived from zero-seed solutions. Additionally, we derive periodic solutions from non-zero seed solutions. To visualize these solutions, we employ Maple to generate three-dimensional and density diagrams, thereby facilitating a comprehensive understanding of the solution structures within the three-component Dirac–Manakov system. [ABSTRACT FROM AUTHOR]

The aim of this manuscript is to study various optical soliton profiles of the Schrödinger–Hirota (SH) equation having the parabolic law nonlinearity by utilizing the Sardar-Subequation (SSe) method. First, the general method of the suggested SSe method is presented. Then using traveling wave transformation the suggested equation is converted into the nonlinear ordinary differential equation, where the real and imaginary parts are separated. Furthermore, the proposed method is utilized and novel optical solitons of the suggested SH equation with parabolic law are obtained. Furthermore, the solutions are validated through stability analysis. The exact analytical solutions are graphically simulated where the effects of different parameters on the soliton wave profiles are studied. [ABSTRACT FROM AUTHOR]

This manuscript elaborate a novel characteristic of stochastic multi breather type, periodic, hybrid periodic and different type of waves solutions for the Shrödinger–Hirota (SH) equation. The mentioned equation is studied by a Wiener process and white noise which is used for the sudden and large-scale fluctuation. By applying the wave transformation technique the considered equation is transformed into ordinary differential equations, gives meaningful analysis. From the solution of the SH equation various type of results, including breather like waves, hybrid periodic waves, and singular solitons. Breather waves are applied in optical fiber communications, oceanography, and plasma physics. Singular waves find use in medical imaging, seismic research, and nonlinear optics. Hybrid singular-periodic waves have applications in photonics, acoustics, and material science, enabling advancements in diverse fields. To visually capture these intricate behaviors, we used Mathematica software to generate 2D and 3D graphs of the analytical stochastic solutions. This combination of mathematical rigor and numerical simulations provides a comprehensive understanding of the phenomena under study, making a valuable contribution to the field of nonlinear wave equations and stochastic processes. [ABSTRACT FROM AUTHOR]

In this article, the modified extended direct algebraic method is applied for the perturbed highly dispersive nonlinear Schrödinger equation with conformable fractional derivative and sextic-power law refractive index. Various types of solutions are extracted such as bright solitons, dark solitons, combo bright-dark solitons, singular solitons, singular periodic wave solutions, exponential wave solutions and rational solutions. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. [ABSTRACT FROM AUTHOR]

In this research work, we explored the unexpected optical soliton and solitary wave to the nonlinear (2+1)-dimensional Zakharov–Kuzetsov equation by utilizing the auxiliary equation method. The explored optical soliton and solitary wave solutions obtained in variety of soliton including bright solitons, anti-kink wave solitons, periodic optical solitons, kink wave solitons, dark solitons, anti-kink dark solitons, combined solitons, crest-turf form solitons, peakon solitons and periodic solitary waves. The physical structure of extracted optical solitons visualized in three-dim, two-dim and contour plotting by utilizing the numerical simulations with computational software Mathematica. The secured optical solitons will be play important role in the investigation of nonlinear (2+1)-dim Zakharov–Kuzetsov equation and will be develop interest in the researchers for further investigation on this nonlinear model. The physical structure of explored soliton results show that, these solitons will be play important role in the areas of sciences and engineering such as nonlinear optics, transmission system, communication system, nonlinear dynamics, soliton wave theory and ocean engineering. The successful investigation is the witness that the proposed approach is effective, efficient and powerful for the exploration of solitary waves special verities of optical solitons to the various kinds of nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The concern of this study is to investigate the optical solitons pluses. The (2 + 1) -dimensional Kundu–Mukherjee–Naskar (KMN) mathematical model in birefringent fibers is taken under consideration for this sake because this model has great importance in optics and delineate the propagation of soliton dynamics in optical fiber communication system and the rogue waves in the oceans and the bending of the light beam. Two newly developed approaches first extended rational sinh-Gordon method which is formulated from the well-known sinh-Gordon equation and second exp (− ϕ (ϖ)) -expansion function method are manipulated for the construction of optical solitons in distinct formats. Bright, dark, and singular along their combined forms, periodic and plane wave solutions are extracted with the aid of proposed methods. Moreover, the modulation instability of investigated model is also carried out via linear stability theory. To endorse the physical compatibility of the results, the 2D, 3D, contour, and density plots have been delineated using appropriate parametric values. According to our literature research, these two methods that we are working on have not been applied to the KMN equation in birefringent fibers before, and we believe that the new solutions we have obtained will be useful to researchers working in modeling in this field. The evaluated results suggested that the techniques employed in this research to recover inclusive and standard solutions are approachable, efficient, and speedier in computing and can be considered a handy tool in solving more complex phenomena with the assistance of symbolic computation. [ABSTRACT FROM AUTHOR]

This paper explores the truncated M-fractional three-component coupled nonlinear Schrödinger (tc-CNLS) equation, that regulates the behavior of optical pulses in optical fibers. These equations are utilized in various scientific and engineering fields, including nonlinear fiber optics, electromagnetic field waves, and signal processing through optical fibers. The study of multi-component NLS equations has gained significant attention due to their ability to elucidate various complex physical phenomena and exhibit more dynamic structures of localized wave solutions. The freshly invented integration tools, known as the fractional modified Sardar subequation method (MSSEM) and fractional enhanced modified extended tanh-expansion method (eMETEM), are employed to ensure the solutions. The study focuses on extracting various types of optical solitons, including bright, dark, singular, bright-dark, complex, and combined solitons. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. The utilized methodology is effective in explaining fractional nonlinear partial differential equations (FNLPDEs) as it offers pre-existing solutions and additionally derives novel exact solutions by mixing outcomes from various procedures. Furthermore, we plot the visualizations of solutions by plotting 3D, 2D, and contour graphs with the corresponding parameter values. The findings of this paper can improve the understanding of the nonlinear dynamical behavior of a specific system and demonstrate the efficacy of the methodology used. We anticipate that our study will provide substantial benefits to a considerable group of engineering model experts. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems. [ABSTRACT FROM AUTHOR]

The nonlinear Kadoma equation with M-truncated derivatives (NLKE-MTD) is taken into consideration here. By using generalized Riccati equation method (GRE method) and Jacobi elliptic function method, new hyperbolic, rational, trigonometric and elliptic solutions are discovered. Because the NLKE is widely employed in optics, fluid dynamics and plasma physics, the resulting solutions may be used to analyze a wide variety of important physical phenomena. The dynamic behaviors of the different derived solutions are interpreted using 3D and 2D graphs to explain the effects of M-truncated derivatives. We may conclude that the surface moves to the right as the order of M-truncated derivatives increases. [ABSTRACT FROM AUTHOR]

In this research article, the dynamics of optical solitons in cascaded system with spatio-temporal dispersion is discussed. The Kerr medium is considered for this investigation. Two versatile integration tools have been used to extricate different traveling wave solutions. Rapid convergent approximation method has been employed to extract bright, singular and periodic solitons whereas polynomial function solutions are obtained by unified method. The constraints on the parameters for the validity of these solutions are also provided. Galilean transformation is prosecuted to construct the planer dynamical system of the said model. Runge–Kutta fourth-order technique is used to extract the non-linear periodic waves of the considered problem and consequences are depicted through different portraits. Further, by employing an extrinsic periodic force, chaotic and quasiperiodic pattern of discussed model is analyzed for different values of the parameters. While chaotic and quasiperiodic behaviors are observed for some values of parameters of considered system by keeping the force and frequency of the perturbed dynamical system fixed. Sensitive anatomy is carried out for diverse initial value problems. It is investigated that the chaotic and quasiperiodic pattern is present in the perturbed dynamical system. [ABSTRACT FROM AUTHOR]

The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevé test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrödinger equations and may be used for the description of optical solitons in a nonlinear medium. [ABSTRACT FROM AUTHOR]

This article studies high dispersion solitons in optical couplers that are composed of metamaterials using the modified extended direct algebraic method (MEDAM). Different dynamic behaviors of unique soliton waves that include singular and combo-soliton solutions are raised using the MEDAM. The solutions that are produced include singular periodic solutions, bright and dark soliton solutions, Jacobi elliptic functions, and singular soliton solutions. Furthermore, the physical depiction of the found solutions is given through contour graphs, 2D, and 3D graphics. The main objective of this paper is to incorporate meta-materials into a governing model for highly dispersive solitons in optical couplers. The modified extended direct algebraic technique, reveals several solitons, where the uniqueness is found. Moreover, by the end of this work, we present 2D, 3D, and contour charts of the various obtained solutions to further highlight our findings. [ABSTRACT FROM AUTHOR]

This study delves into a complex mathematical model, namely the fractional Chen–Lee–Liu (FCLL) model in birefringent fibers which has two components in the form of vector solitons in optical fiber. The FCLL model has remained a uniform fascination for scientists due to its energetic significance in the study of circuit design, signal processing, secure communications, encryption and decryption of chaotic signals, as well as in plasma physics. For the intellectual curiosity of new precise solutions of the selected model, two innovative norms namely, the modified Sardar-sub equation scheme and the improved F -expansion method have been suggested in the sense of a M-truncated derivative. By employing the aforementioned strategies the bright, dark, bright-dark, periodic, combo, singular, mixed trigonometric, hyperbolic, exponential as well as rational soliton solutions are segregated. Moreover, we examined the sensitivity analysis of selected model. By selecting appropriate parameters, numerical simulations of the attained outcomes are sketched as interesting figures that present the meaning of the obtained results. The generated outcomes are optimistic, demonstrating that the selected approaches are robust, categorical, and efficient in discovering novel solutions to the variety of complex nonlinear models that have arisen in the recent phase of applied sciences. [ABSTRACT FROM AUTHOR]

Studying the highly dispersive model with arbitrary refractive index initiated by Kudryashov is the subject of this work. This model depicts the behavior of soliton propagation via polarization-preserving fibers. To secure a dark soliton and like-solitons with singularities solution for the proposed model, the generalized Kudryashov's integration approach has been utilized. This method do not have any constraints on how to find solutions. Some significant solutions have been graphically elaborated in the form of 2D and 3D plots by selecting the appropriate parameters to provide a better physical illustration and understanding of the dynamical physical properties of this model. [ABSTRACT FROM AUTHOR]

This paper introduces a novel model proposed by Wazwaz et al. in 2023, in the nonlinear optics literature. This contributes to advancing optical devices and technologies, particularly in telecommunications and laser systems. The characteristics of bright, dark, and periodic soliton solutions for the (2+1)-dimensional nonlinear Schrödinger equation with fourth-order nonlinearity and dispersion are explored in this paper. The relevance of these solutions lies in the study of nonlinear waves propagating in an inhomogeneous optical fiber. The soliton solutions are obtained through the implementation of three analytical methods: the Kudryashov method, the Bernoulli Sub-ODE method, and the Extended Direct Algebraic method. The bright, dark, and periodic soliton solutions are constructed by utilizing bilinear forms. Furthermore, the impact of variable coefficients on the structures of these solitons is analyzed. Graphical illustrations depict the propagation of bright, dark, and periodic solitons. [ABSTRACT FROM AUTHOR]

This study explores optical soliton solutions within the framework of the Caudrey–Dodd–Gibbon equation (CDGE) and the ( 1 + 1 )-dimensional Boussinesq equation, utilizing the modified Sardar sub-equation method (MSSEM). The derived solutions are meticulously verified using symbolic software Mathematica and encompass a rich array of mathematical functions, including trigonometric, hyperbolic, and exponential functions. Visualization techniques, such as 3D plots, 2D plots, density graphs, and contour graphs, effectively illustrate the diverse behaviors exhibited by these soliton solutions. These equations have been studied previously, their comprehensive traveling wave solutions are relatively unexplored. By employing the modified Sardar sub-equation method, which has demonstrated effectiveness in solving nonlinear evolution equations, this study aims to bridge this gap. The soliton solutions obtained encompass a wide spectrum of behaviors, including bright, dark, periodic, singular, dark-periodic, bright-periodic, dark-singular, compactons, and bright-singular soliton solutions, as well as other complex phenomena. The comprehensive exploration of soliton solutions not only enhances our understanding of fundamental wave phenomena but also provides valuable insights for addressing nonlinear equations across various scientific disciplines, including optical fiber communications, plasma physics, and nonlinear dynamics. [ABSTRACT FROM AUTHOR]

In an optical fiber, we report on our study of pulse compression using an analytical method. A significant role for the eighth order nonlinear Schrödinger (NLS) equation may be seen in the study of ultra-short pulses, in particular extremely nonlinear optical phenomena. As a result of our study, which plays a significant role in reviving potent mathematical procedures, such as the extended rational sinh–cosh method for obtaining the dark soliton solution and the cosine method for solving the NLS equation to attain M-shaped, W-shaped soliton structure, dark and bright solitonic structure. Solitons are shown to have a strictly chirp-free structure, which facilitates effective compression. According to the results, wavevector may effectively regulate the shape and propagation behavior of soliton. [ABSTRACT FROM AUTHOR]

In this research work, we utilized the auxiliary equation technique and extracted the optical soliton solutions to the nonlinear longitudinal wave equation (NLLWE) in magneto electro elastic (MEE) rod that was spread out in a circle. The NLLWE in MEE systems deals with the mathematical physics of transverse Poisson's effect dispersal and also very important in many engineering fields like sensors and actuators. As a result, we extracted the exact soliton solutions in bright solitons, dark solitons, kink wave solitons, anti-kink wave solitons, combined bright-dark solitons, solitary waves and periodic singular solitons. The physical structure of some extracted solutions visualizing in contour, two, and three dimensions through numerical simulation. The explored soliton solutions are interested, more general and having different physical structure, which may will be helpful to study of physical phenomena in the fields of optical fibers, plasma physics, soliton wave theory, nonlinear optics, ocean engineering, nonlinear dynamics and different branches of applied sciences. The successful extraction of exact solitons shows that this utilized approach is effective, straightforward, concise and powerful can also applicable to other nonlinear partial differential equations that involve in mathematical physics, engineering and applied sciences. [ABSTRACT FROM AUTHOR]

This study addresses the damped (2 + 1)-dimensional nonlinear Schrödinger equation (DNLS) using innovative techniques, with a focus on elucidating the problem's significance, employed methodologies, key findings, and unique contributions. We extensively explore the modified exponential rational function technique and other distinctive approaches, revealing a diverse range of wave solutions for DNLS equation. Notably, our research unveils new optical solutions, including bright and dark solitons, extracted under specific parameter conditions. The significance of this work is underscored by its contributions to nonlinear dynamics and optical physics. Our findings provide valuable insights into the intricacies of the DNLS equation, surpassing prior endeavors in the field by introducing novel methodologies and uncovering a wealth of solutions with broad applicability. [ABSTRACT FROM AUTHOR]

In this article, the Bernoulli sub-ODE and generalized Kudryashov methods have been successfully used to look for travelling wave solutions for the coupled non-linear evolution equations including the coupled Higgs equation and the Maccari system. The aforementioned approaches provide more new broad solutions than the previous ones now in use and are straightforward to apply. In both techniques, a travelling wave transformation is employed to convert non-linear partial differential equations into an ordinary differential equation. The solitary wave solutions are also generated from the travelling wave solutions when the parameters are considered as unique values. Several soliton solutions are generated for various parameter combinations. Numerous innovative solutions have been created by using Bernoulli sub-ODE and generalized Kudryashov approaches, including the periodic wave, kink wave, bell shape, anti-bell shape, M-shape, V-shape, W-shape, Z-shape, bright, dark and singular soliton solutions. To demonstrate how the Bernoulli sub-ODE and generalized Kudryashov approaches can be used to uncover the analytical solutions of the coupled Higgs equation and the Maccari system, replicate many figures in computer software Mathematica 13.2 along with several 3D, 2D, and contour plots. The similarities, contrasts, advantages and disadvantages of the two analytical techniques are examined. It has been demonstrated that the travelling wave solutions generated by these two analytical techniques, each using a different basis equation, have unique characteristics. The outcomes show that the methods used may reliably identify wide-spectral stable travelling wave solutions to non-linear evolution equations that appear in a variety of scientific, technical, and engineering disciplines. [ABSTRACT FROM AUTHOR]

In this research work, we extracted the variety of newly optical soliton solutions which describe the wave propagation in nonlinear low-pass electrical transmission lines model by utilizing the auxiliary equation method. The secured solitons solutions yield a variety of typical soliton shapes, including dark solitons, periodic singular optical solitons, combined bright and dark solitons, kink wave solitons, bright solitons, ant-kink wave solitons, and solitary waves. The physical structure of extracted soliton solutions visualized in three different graphically structures such as three-dimension, two-dimensional and contour plotting on the choices of some constant parameters by utilizing the numerical simulations. This study explored optical solitons, solitary wave solutions, exact solitons for improving the performance of nonlinear low-pass electrical transmission systems. It provides an overview of solitons, their relevance, and stability principles. It also presents the mathematical formulation of the nonlinear low-pass electrical transmission lines model and discusses its implications for signal propagation. The secured soliton solutions have many applications in engineering and science such as nonlinear optics, fiber optics, laser optics, nonlinear dynamics, ocean engineering, electronic engineering, electrical engineering, computing engineering, power engineering and several other different kinds of physical sciences. The whole study shows that the suggested method is more powerful, effective, simple, and strong for looking into different types of nonlinear models involve in nonlinear sciences and the engineering presentation field. [ABSTRACT FROM AUTHOR]

In this paper, we explore new optical solitons for the coupled nonlinear Schrödinger equation with generalized anti-cubic nonlinearity, which governs the propagation of electromagnetic waves in magneto-optic waveguides. These components play a crucial role in optical transmission lines and lasers, being utilized in integrated optical circuits as modulators, circulators, and isolators. To retrieve optical soliton solutions, we have implemented, for the first time, two powerful schemes for the model equation, namely the modified Sardar sub-equation method and the new Φ6-model expansion method. As a result, we obtained a wide variety of new soliton solutions, including bright, dark, gray, dark bell-type, kink, anti-kink, singular, mixed bright-singular, and dark-singular solitons. Additionally, various other solution forms emerged, such as Jacobi elliptic functions, periodic, and rational solutions. Finally, by extracting parametric conditions for the existence of soliton solutions, we discovered that physical parameters, including inter-modal dispersions, self-steepening effect, nonlinear dispersion, and the magneto-optic effect, play a crucial role in both the existence and shaping of the extracted solitons. [ABSTRACT FROM AUTHOR]

In this paper, we look at higher-order nonlinear Schrö dinger equation (HONLSE) through stochastic sense. This equation is examined in the presence of Brownian motion and noise term. Using the robust solver, we generate several new crucial stochastic solutions for the HONLSE. During fibre transmissions, the HONLSE coefficients, such as nonlinearity, dispersion and noise term, influenced the solitonic picture. The solitary properties of communication fibers were altered by higher-order features. To illustrate how these optical solutions behave physically, certain representations of the acquired solutions as super and shock-like shapes are introduced. The presented research can be extended to other nonlinear equations with comparable properties. [ABSTRACT FROM AUTHOR]

This study aims to obtain the optical soliton solutions of the stochastic perturbed Radhakrishnan–Kundu–Lakshmanan equation which models the optical solitons in optical waveguides such as silica fibers with Kerr law in the presence of chromatic and third-order dispersions by multiplicative white noise in Itô calculus. The study constitutes one of the works aimed at adapting the model in accordance with the importance of the noise effect in nonlinear optics. In the first step, the nonlinear ordinary differential form of the investigated problem has been obtained by using an appropriate complex wave transformation. The enhanced Kudryashov technique, which is the combination of Kudryashov and the new Kudryashov methods, is applied to the nonlinear ordinary differential form. As the result, bright, dark and singular stochastic soliton solutions of the analyzed problem have been carried out by assigning appropriate parameter values and the impact of noise effect on the soliton behavior has been investigated. Lastly, the graphical representations and required comments have been presented in the related sections. [ABSTRACT FROM AUTHOR]

This research explores the dual-mode manifestation within the nonlinear Schrödinger equation, elucidating the amplification or absorption of paired waves. This study delves into the simultaneous generation of two distinct waves associated with the dual-mode phenomenon with three crucial parameters: phase velocity, nonlinearity and dispersive factor. The resulting wave phenomena from these solutions have implications across various fields, including fluid dynamics, water wave mechanics, ocean engineering and scientific inquiry. The study employs the modified Sardar sub-equation method to obtain the optical soliton solutions, encompassing various types such as dark, bright, singular, combo dark–singular, periodic singular and dark–bright solitons. The obtained results highlight the reliability and simplicity of the modified Sardar sub-equation method. Additionally, the paper delves into the parametric conditions crucial for shaping and sustaining these solitons. The research explores the interaction of dual waves and the variation in wave speed. Furthermore, dynamic phenomena are illustrated, and the physical implications of the solutions are interpreted using 3D and 2D plots with different parameter values. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is a fundamental equation in the field of nonlinear optics and plays an important role in the study of many physical phenomena. The present study introduces a new model that demonstrates the novelty of the paper and provides the advancement of knowledge in the area of nonlinear optics by solving a challenging problem known as the extended (3 + 1)-dimensional nonlinear conformable Kudryashov's equation (CKE) with generalized anti-cubic nonlinearity, which is a generalization of the NLSE to three spatial dimension and one temporal dimension for the first time. This work is significant because it advances our understanding of nonlinear optics and its applications to solve complex equations in physics and related disciplines. The extended hyperbolic function method (EHFM) and Nucci's reduction method are applied to the extended (3 + 1)-dimensional nonlinear CKE with generalized anti-cubic nonlinearity. The equation is solved by using the concept of conformable derivative, a recently developed operator in fractional calculus, which has advantages over other fractional derivatives in terms of accuracy and flexibility. The attained solutions include periodic singular, dark 1-soliton, singular 1-soliton, and bright 1-soliton which are visualized using 3D and contour plots. This study highlights the potential of using conformable derivative and the applied techniques to solve complex nonlinear differential equations in various fields. The obtained solutions and analysis will be useful in the design and analysis of optical communication systems and other related fields. Overall, this study contributes for the understanding of the dynamics of the extended (3+1)-dimensional nonlinear CKE and offers new insights into the use of mathematical techniques to tackle complex problems in physics and related fields. [ABSTRACT FROM AUTHOR]

The primary focus of this paper is the investigation of the truncated M fractional Kuralay equation, which finds applicability in various domains such as engineering, nonlinear optics, ferromagnetic materials, signal processing, and optical fibers. As a result of its capacity to elucidate a vast array of complex physical phenomena and unveil more dynamic structures of localized wave solutions, the Kuralay equation has received considerable interest in the scientific community. To extract the solutions, the recently developed integration method, referred to as the modified generalized Riccati equation mapping (mGREM) approach, is utilized as the solving tool. Multiple types of optical solitons, including mixed, dark, singular, bright-dark, bright, complex, and combined solitons, are extracted. Furthermore, solutions that are periodic, hyperbolic, and exponential are produced. To acquire a valuable understanding of the solution dynamics, the research employs numerical simulations to examine and investigate the exact soliton solutions. Graphs in both two and three dimensions are presented. The graphical representations offer significant insights into the patterns of voltage propagation within the system. The aforementioned results make a valuable addition to the current body of knowledge and lay the groundwork for future inquiries in the domain of nonlinear sciences. The efficacy of the modified GREM method in generating a wide range of traveling wave solutions for the coupled Kuralay equation is illustrated in this study. [ABSTRACT FROM AUTHOR]

The paper focuses on investigating the time-fractional (3 + 1)-dimensional cubic and quantic nonlinear Schrödinger equation. We adopt the novel Kudryashov method to generate a distinct class of optical solutions for the current conformable fractional derivative problem. Our method explores various solution forms, including dark, wave, mixed dark-bright, and singular solutions. The soliton solutions we construct are visually represented to illustrate the influence of the fractional order derivative. Further, we elucidate the influence of solution parameters on the wave envelope, providing clear interpretations through 2D graphics presentations. The results underscore the efficacy of our approach in discovering exact solutions for nonlinear partial differential equations, especially in cases where alternative methods prove ineffective. The significance of the present paper lies in its contribution to advancing the understanding of the behavior of optical solutions in nonlinear systems, providing valuable insights for both theoretical and practical applications. In the field of nonlinear optics, this equation can describe the propagation of optical pulses in nonlinear media. It helps in understanding the behavior of intense laser beams as they propagate through materials exhibiting nonlinear optical effects such as self-focusing, self-phase modulation, and optical solitons. [ABSTRACT FROM AUTHOR]

This investigation focuses on the construction of novel dark and singular soliton solutions for the Hirota equation, which models the propagation of ultrashort light pulses in optical fibers. Initially, we employ a wave variable transformation to convert the physical model into ordinary differential equations. Utilizing extended rational sinh–cosh and sine–cosine techniques, we derive an abundant soliton solution for the transformed system. By plugging these explicit solutions back into the wave transformation, we obtain dark and singular soliton solutions for the Hirota equation. The dynamic evolution of dark soliton profiles is then demonstrated, with a focus on varying physically significant parameters such as wave frequency, strength of third-order dispersion, and wave number. Furthermore, a comprehensive analysis is examined to elucidate how the dark and singular soliton profiles undergo deformation in the background influenced by these arbitrary parameters. The findings presented in this study offer valuable insights that could potentially guide experimental manipulation of dark solitons in optical fibers. [ABSTRACT FROM AUTHOR]

Optical soliton is a physical phenomenon in which the waveforms and energy of optical fibers remain unchanged during propagation, which has important application value in information transmission. In this paper, the coupled nonlinear Schrödinger equations describe the propagation of optical solitons with different frequencies in sense of local fractional derivative is analyzed. The exact traveling wave solutions of the non-differentiable type defined on the Cantor sets are obtained. The characteristics of the particular solutions of fixed fractal dimension are discussed. It is proved that the local fractional coupled nonlinear Schrödinger equations can describe the interaction of fractal waves in optical fiber transmission. [ABSTRACT FROM AUTHOR]

The generalized nonlinear Schrödinger equation with M-truncated derivatives (GNLSE-MTD) is studied here. By using generalized Riccati equation and mapping methods, new elliptic, hyperbolic, trigonometric, and rational solutions are discovered. Because the GNLSE is widely employed in communication, heat pulse propagation in materials, optical fiber communication systems, and nonlinear optical phenomena, the resulting solutions may be used to analyze a wide variety of important physical phenomena. The dynamic behaviors of the various derived solutions are interpreted using 3-D and 2-D graphs to explain the affects of M-truncated derivatives. We can deduce that the surface shifts to the left when the order of M-truncated derivatives decreases. [ABSTRACT FROM AUTHOR]

We investigate the stable propagation of 1D and 2D optical solitons in nonlinear Schrödinger equation with fourth-order diffraction and self-focusing power-law nonlinearity in the presence of complex generalized Scarff-II P T -symmetric potential. Using both analytical and numerical techniques, we identified that the stability of the 1D and 2D optical solitons are determined by the strength of the fourth-order diffraction. For weak fourth-order diffraction, the stable and unstable optical solitons are observed for various ranges of localization parameter which is present in the considered complex P T -symmetric potential. The soliton is stable for almost all the values of the localization parameter with strong fourth-order diffraction. We have also discussed the impact of power-law nonlinearity on the stability of 1D and 2D optical solitons. The stable dynamical evolution of 1D and 2D optical solitons is also shown for both weak and strong fourth-order diffraction in the presence of power-law nonlinearity and complex generalized Scarff-II P T -symmetric potential. [ABSTRACT FROM AUTHOR]

In the field of nonlinear optics, soliton structures have been extensively investigated in recent years. Optical solitons can be used in communication systems as optical information carriers. The advantage of a optical soliton is that it does not alter its structure when it interacts with other pulses. Optical solitons are useful for signal processing applications like pulse compression, regeneration, and amplification, leading to cleaner, more reliable signals. They can also be explored in optical computing, sensing, and laser technology. Studying optical solitons provides insights into nonlinearity and dispersion in wave propagation, contributing to physics and paving the way for future discoveries. The purpose of this article is to strive for the optical soliton solutions of the Manakov model with the help of the modified auxiliary equation method and the extended trial equation method. The Manakov model is a simple, analytical, and numerical model that provides basic insights into soliton formation and propagation. This model is suitable for studying soliton properties like stability, interactions, and collisions. The study provides hyperbolic, trigonometric, rational, and notably, Jacobi-elliptic function solutions, which have not been explored for the considered system. Additionally, dark soliton, bright soliton, bright singular soliton, bright singular two-solitons, multi solitons and periodic solitary wave solutions are exhibited by their graphical representations. [ABSTRACT FROM AUTHOR]

This research paper's primary goal is to find fresh approaches to the Hirota–Maccari system. This system explains the dynamical features of the femto-second soliton pulse in single-mode fibers. The bright soliton, dark soliton, dark-bright soliton, dark singular, bright singular, periodic soliton, and singular solutions are developed utilizing the modified auxiliary equation technique. To make the physical significance of each unique solution clearer, it is mapped in both 2D and 3D. The primary Hirota–Maccari system is being verified by all new solutions, and the constraint condition is also provided. The obtained optical solitons may be important for the analysis of nonlinear processes in optic fiber communication and signal processing. [ABSTRACT FROM AUTHOR]

In this research article, the stochastic complex Ginzburg–Landau equation with Kerr law nonlinearity and chromatic dispersion is studied, which has been the focus of many studies and continues to be important in this field of study of nonlinear optics. The improved modified extended tanh technique is utilized in this work. This method depends on the extended Riccati equation. So, numerous stochastic exact solutions including singular solitons, dark solitons, bright solitons, exponential solutions and singular periodic solutions are offered by this method. This technique presents a realistic and successful strategy for deriving exact solutions to various nonlinear partial differential equations. Graphical representations of some of the extracted solutions using different noise intensities are shown to demonstrate the influence of the noise. The optical solitons produced in respect to this form have never been explored by the proposed technique before, and the results have never been published. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to study the optical soliton solutions and single traveling wave solutions of the generalized stochastic Schrödinger–Hirota equation in magneto-optic waveguides. With the help of the complete discriminant system technique and symbolic computation, a range of new single traveling wave solutions and optcial solitons are derived, which include Jacobian elliptic function solutions, dark solitons, trigonometric function solutions, singular solitons, rational function solutions, hyperbolic function solutions, periodic wave solutions and solitary wave solutions. Lastly, in order to understand mechanisms of complex physical phenomena and dynamical processes for the generalized stochastic Schrödinger–Hirota equation in magneto-optic waveguides, two-dimensional and three-dimensional diagrams are also drawn. [ABSTRACT FROM AUTHOR]

This work explores the effect of fractional derivative on the fourth-order nonlinear Schrödinger equation with Kerr law nonlinearity, a highly significant equation in the study of wave propagation in dispersive media. By employing the improved modified extended tanh-function method, a variety of optical soliton solutions are derived. These solutions including dark solitons, bright solitons, and singular solitons. Moreover, singular periodic solutions and exponential solutions are raised. These solutions offer valuable insights into the dynamic behavior of nonlinear wave phenomena. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. Bright and dark solitons, pivotal components of our findings, play a critical role in fiber optics by facilitating the transmission of high-power optical signals with exceptional attributes such as shape preservation. These properties eliminate the need for external pulse compression, simplifying the design and operation of optical systems. The outcomes of this study contribute in advancing our knowledge of wave propagation in dispersive media and have practical implications for the development of efficient and robust optical communication technologies. [ABSTRACT FROM AUTHOR]

This study investigates the application of the novel Kudryashov approach to a time-fractional nonlinear Schrödinger model featuring second-order spatiotemporal and group velocity dispersion coefficients. Various exact solutions for this model in optical fibers are established, utilizing hyperbolic and exponential functions. These solutions encompass diverse optical solitons, such as bright, singular, bell-shaped, mixed dark-bright, dark-bright, and wave solitons. To assess the significance of the time-fractional nonlinear Schrödinger model and illustrate the different forms of these innovative optical solutions, contour plots, three-dimensional plots, and two-dimensional plots are presented. Furthermore, the influence of the conformable fractional order derivative on a specific category of the new optical solutions is explored through illustrative graphs, emphasizing the impact of fractional parameters. The primary objective of this paper is to elucidate the significant influence of the conformable fractional derivative parameter on the Schrödinger equation, particularly in shaping various physical aspects of signal propagation in optical fiber. Understanding and manipulating this parameter provide opportunities for optimizing optical fiber systems for specific applications. Moreover, the proposed technique demonstrates its reliability as a tool for examining analytical solutions of fractional differential equations. The introduced Schrödinger model holds potential applications in the transmission of ultra-fast pulses through optical fibers. [ABSTRACT FROM AUTHOR]

The use of optical fiber for communication has grown at a rapid pace due to the demands of the modern information era. In this paper, the modified extended direct algebraic method is implemented to explore optical solitons and other exact wave solutions for the coupled system of perturbed highly dispersive complex Ginzburg–Landau equation with polynomial nonlinearity law which describe the transmission of solitons in birefringent fibers. The obtained solutions include bright solitons, dark solitons, singular solitons and combo dark-singular solitons. Additionally, Jacobi elliptic function solutions, exponential solutions, and singular periodic solutions are also offered. To ensure the existence of the obtained soliton solutions, we set some constraints on the parameters. In addition, some selected solutions are visually shown to demonstrate the physical properties of the exact solutions. [ABSTRACT FROM AUTHOR]

This current research explores a new generalized q-deformed sinh -Gordon equation. The governing equation is frequently used to model plasma-based solutions, complex optical science, photonic transmission systems, ultrashort burst lasers to identify objects and other theoretical sciences. The work consists of two goals. Firstly, analytically using the modified extended tanh function approach. Precise results for the derived equation are obtained that could be used to simulate physical systems with broken symmetries and to consider events involving amplification or dissipation. Secondly, with the help of a numerical approach investigate the error function between the q-demormed terms. Several figures have been included to illustrate the different optical solitons propagation patterns. [ABSTRACT FROM AUTHOR]

This paper delves into an investigation of the Kuralay model, with a particular emphasis on the Kuralay-II system. The primary objective of this research is to analyze the integrable motion of space curves generated by these equations. The proposed equation can be classified as a type of nonlinear Schrödinger equation, generates integrable long short waves models and enhances our knowledge of optical soliton dynamics in different physical systems. The novelty of this research lies in the utilization of three distinct methodologies, namely the unified solver method, e x p (- χ (η)) approach, and ansatz methods, for extracting optical soliton solutions to these equations. These solutions take the form of dark, bright, singular, and periodic optical solitons. In order to provide an understanding of these optical soliton solutions, we present 3D, 2D, and density plots to elucidate the physical characteristics. Furthermore, we provide a comparative analysis of the employed techniques. The outcomes obtained may also prove beneficial for shaping future modeling endeavors. The techniques employed in this study have demonstrated their effectiveness, and reliability in addressing additional non-linear partial differential equations. [ABSTRACT FROM AUTHOR]

The complex nonlinear Fokas–Lenells (FL) equation to obtain the explicit travelling wave solutions under different values parameters such as solitary wave solutions, kink solitary wave solutions and periodic wave solutions and others solutions are studied using the dynamical system approach. Also, the optical solitons for the FL equation, as well as the plane-wave, complex dark-singular, and complex periodic-singular solutions are obtained via the e x p (- Φ (ζ)) expansion method. In conclusion, graphical representations of these solutions are provided so that the dynamics of these waves can be viewed. [ABSTRACT FROM AUTHOR]

One of the natural consequences of soliton propagation is a birefringence phenomenon occurring due to bending, twisting or rough handling of fibres, which produce a bit of detrimental effect. In this research, we find optical soliton solutions and other exact solutions for the high-order coupled nonlinear Schrödinger system which describe the transmission of solitons in birefringent fibers. The study is conducted with the aid of the improved modified extended tanh function method. A variety of distinct traveling wave solutions are furnished. The obtained solutions include dark solitons, bright solitons, and singular solitons. Additionally, hyperbolic solutions, periodic solutions, singular periodic solutions, rational solutions, exponential solutions, Jacobi elliptic function solutions and Weierstrass elliptic doubly periodic type solutions are also offered. To help readers physically grasp the acquired solutions, graphical representations of some of the extracted solutions are provided. [ABSTRACT FROM AUTHOR]

The nonlinear space–time fractional Sasa–Satsuma and Schrödinger–Hirota equations with beta derivative describe optical soliton, photonics, plasmas, neutral scalar masons, and long-surface gravitational waves in the real world. Through the fractional wave transform, the models are converted into a single wave variable equation. In this article, we examine a range of compatible, useful, and typical wave solutions expressed in the forms of hyperbolic, trigonometric, and rational functions uniformly through the ( Q ′ / Q , 1 / Q )-expansion approach. When specific parameter values are set, the generalized wave solutions exhibit a wide range of shapes, including asymptotic, anti-asymptotic, dark-optical, breather, lump-periodic, kink, kink-bell-shaped, homoclinic-breather, bright, dark, and periodic solitons that resemble periodic breathing patterns. We also investigate the effect of the fractional parameter δ into the wave profile, revealing a clear correlation between changes in the fractional order derivative δ and variation in the soliton's shape. The results underscore the use of this approach for the exploration of diverse nonlinear fractional systems within the context of beta derivatives. Varying the fractional-order δ and maintaining specific fixed parameter values, we depict 3D-surface, 2D-surface, density, and contour plots to visualize some of the derived solutions. [ABSTRACT FROM AUTHOR]

Extremely short pulse propagation in optical fiber is modelled via using the higher order nonlinear Schrödinger equation (NLSE) with cubic quintic nonlinearity. To construct singular bright, kink, and anti-kink solitons, periodic waves as well as multi-peak and breather type waves of generalized NLSE in a cubic quintic non-Kerr medium, we used a generalised exponential approach. In physics and applied mathematics, the obtained solutions have significant applications. We have also discussed the solitary wave parameters under which dark and bright solitons may develop in this medium. In order to visualise the physical phenomena of this model, we have provided a graphic representation of the movements of the created solitary wave and soliton solutions. This reliable, effective, and successful strategy may also be used to solve many other similar sorts of models that arise in applied sciences. [ABSTRACT FROM AUTHOR]

Nonlinear Schrödinger model is one of the important fundamental nonlinear physical model to describing the fluctuations development of optical solitons and play a important role in the demonstration of dynamical fiber optics. Therefore, in nonlinear dispersive media the propagation of waves are the area of considerable interest due to its large range of possibilities to the ultrafast light pulses and data processing in communication systems. In this research, we investigated the one of the important class of nonlinear Schrödinger equation named modified unstable nonlinear Schrödinger equation (mUNLSE), which describe time periods disturbances in slightly stable and unstable medium, and also manage the instabilities of train form modulated waves. The mUNLSE is a valuable model for understanding wave behavior in fiber optics, aiding engineers in optimizing optical fiber design and predicting various conditions. We explored the collection of optical solitons and solitary wave structures to examine the dynamical properties of the governing model on the base of powerful unified approach. The explored optical solitons demonstrated in 2D, 3D, and contour plots under the aid of computing software Mathematica and may helpful for studying the waves phenomena in nonlinear optics, solitons wave theory, optical fiber, fluid dynamics, communication system, signal transmission, computer networking, sound and heat processing system. Also, the present work provide understanding into the fundamental properties of optical solitons solutions in mUNLSE, and also its experimental consequences in the physically system. On the base of this study, the proposed approach can be utilized to study the other real and complex nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

This study introduces a novel truncated Mittage–Leffler (M)- proportional derivative (TMPD) and examines its impact on the perturbed nonlinear Schrödinger equation (PNLSE) that includes fourth-order dispersion and cubic-quintic nonlinearity. The TMPD-PNLSE is used to model light signals in nanofibers. In addition to dispersion and Kerr nonlinearity, which are characteristics of the NLSE, the PNLSE also exhibits self-steepening and self-phase modulation effects. The unified method is implemented to derive exact solutions for the model equation. These solutions provide a variety of phenomena; including breathers, geometric chaos, and complex solitons. The solutions also exhibit numerous structures, such as geometric chaos, where undulated M-shaped and M-shaped solitons are embedded. The modulation instability is analyzed, finding that it is triggered when the coefficient of the fourth-order dispersion surpasses a critical value. [ABSTRACT FROM AUTHOR]

This paper deals with a new variant of the Biswas–Milovic equation, referred to as the perturbed Biswas–Milovic equation with parabolic-law nonlinearity in spatio-temporal dispersion. To our best knowledge, the considered equation which models the pulse propagation in optical fiber is studied for the first time, and the abundant optical solitons are successfully obtained utilizing the auxiliary equation method. Utilizing a wave transformation technique on the considered Biswas–Milovic equation, and by distinguishing its real and imaginary components, we have been able to restructure the considered equation into a set of nonlinear ordinary differential equations. The solutions for these ordinary differential equations, suggested by the auxiliary equation method, include certain undetermined parameters. These solutions are then incorporated into the nonlinear ordinary differential equation, leading to the formation of an algebraic equation system by collecting like terms of the unknown function and setting their coefficients to zero. The undetermined parameters, and consequently the solutions to the Biswas–Milovic equation, are derived by resolving this system. 3D, 2D, and contour graphs of the solution functions are plotted and interpreted to understand the physical behavior of the model. Furthermore, we also investigate the impact of the parameters such as the spatio-temporal dispersion and the parabolic nonlinearity on the behavior of the soliton. The new model and findings may contribute to the understanding and characterization of the nonlinear behavior of pulse propagation in optical fibers, which is crucial for the development of optical communication systems. [ABSTRACT FROM AUTHOR]

We have studied the dynamics of various kinds of optical dark solitons like, chirped, chirp-free, M-shaped & wing shaped dark solitons using higher-order nonlinear Schrödinger equation. To obtain the exact analytical solution, we employed mathematical techniques such as the extended rational sinh-cosh and sin-cos methods. Our investigation shows that one can manipulate the shape of both chirp and chirp free dark solitons by properly tuning the magnitude of the self steepening and self phase modulation. The stability of the obtained dark soliton solutions are verified by using linear stability analysis. [ABSTRACT FROM AUTHOR]

This study delves into the perturbed Radhakrishnan–Kundu–Lakshmanan ( (p RKL) ) model, a pivotal component within nonlinear optics and communication engineering. In addressing this challenge, we employed the Bernoulli sub-equation function method and the Khater II method as analytical approaches, complemented by numerical solutions authenticated through the exponential cubic B–spline (ECBS) method. Our investigation yielded innovative solitary wave solutions, depicted elegantly through three-dimensional, two-dimensional, and contour plots. To ascertain the precision and dependability of these outcomes, we conducted a comparative analysis between analytical and numerical findings, visually presenting them via two-dimensional graphs. The implications of our discoveries are significant, offering insights into perturbations of optical solitons within nonlinear optical fibers. Our research effectively concludes that the proposed methodologies successfully solve the p RKL model, yielding highly accurate solutions. Notably, our study introduces novelty to nonlinear optics by applying the Bernoulli sub-equation function (BSE) method, the Khater II (Kh II) method, and the exponential cubic B-spline (ECBS) method to the p RKL model, with a specific focus on solitary wave solutions. [ABSTRACT FROM AUTHOR]