Search

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 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]

The topic of dispersive optical solitons is one of the essential areas of telecommunications engineering. This paper presents the nonlinear Schrödinger equation (NLSE) with the cubic-quintic-septic (CQS) law which includes higher-order dispersion terms. This equation examines the dynamics of dispersive optical solitons propagation in nonlinear optical fibers. The presented model is significant in mathematics and theoretical physics sciences because long-distance optical fibers are used in optical communication utilized for transoceanic and intercontinental data transmission. First, the considered equation is transformed into a nonlinear ordinary differential equation (NLODE) using the traveling wave transformation. Then, two powerful techniques, Sinh-Gordon expansion approach and the auxiliary equation method (AEM), based on the homogeneous balance rule, are operated to produce analytical solutions for the NLSE with CQS law. Thus, bright, dark, singular, and periodic-singular soliton solutions are acquired. We demonstrate the three-dimensional (3D) and two-dimensional (2D) representations to interpret the physical behavior of some derived solutions. Besides, we investigate the effects of some parameters in the model with graphical illustrations. Therefore, it can be noted that the obtained soliton solutions have a significant role in soliton dynamics. [ABSTRACT FROM AUTHOR]

This article delves into the study of the perturbed cubic-quartic Kudryashov's equation having the Kudryashov's law of refractive index which is recently introduced to the literature. Utilizing the extended rational sine/cosine and sinh/cosh methods, optical solutions such as dark, periodic, and singular are successfully extracted. The two- and three-dimensional plots of these solutions are demonstrated. Besides, the behavior of solitons and the effects of parameters on wave properties are vividly illustrated to explore how the model's parameters influence these solutions. The findings herein can serve as a positive contribution to future research in nonlinear optics, while the methodology employed can be leveraged for similar nonlinear models in real life. [ABSTRACT FROM AUTHOR]

This paper aims to reveal the effects of the fourth-order dispersion and parabolic law which comes from self-phase modulation on the soliton behavior of the cubic-quartic nonlinear Schrödinger equation (CQ-NLSE) by using the modified new Kudryashov method. First, applying the complex wave transformation, the nonlinear ordinary differential form (NODE) has been obtained. Then, the modified new Kudryashov method (mNKM) has been expressed and applied. In the next step, linear algebraic system has been gained and solved. Then analytical soliton solution of the CQ-NLSE has been derived and checked for accuracy so that it satisfies the main equation. For the obtained solution functions, bright and singular soliton solutions have been gained and their graphical presentations have been made. The effects of both the fourth-order dispersion parameter and the parabolic law nonlinearity on the soliton dynamics have been examined and the necessary comments have been made. To our best knowledge, no such study has been reported for the equation examined. [ABSTRACT FROM AUTHOR]

In this study, an effort has been made to obtain optical soliton solutions of the (1+1)-dimensional Biswas-Milovic equation which was introduced by Biswas and Milovic in 2010, having Kerr law and parabolic-law with weak non-local nonlinearity in the presence of spatio-temporal dispersion, which is one of the important models for nonlinear optics. Although, the model is an equation that has been studied by many researchers, the fact that the form to be examined has not been studied before. As a general algorithm, first converting the model to nonlinear ordinary differential form with a complex wave transformation, then obtaining candidate optical soliton solutions by utilizing the new Kudryashov technique, determining the ones that satisfy the main equation from these solutions as the exact solution, and in order to better understand the obtained solutions by making graphical presentation and providing the necessary comments constitute the main framework of the article. [ABSTRACT FROM AUTHOR]

In the present study, we focus on obtaining the optical soliton solutions of the Drinfeld-Sokolov-Satsuma-Hirota (DSSH) equation using Kudryhashov methods. First, a wave transformation is applied to the DSSH equation, resulting in a nonlinear ordinary differential equation (NLODE). A balance number is deduced through the balancing of this NLODE. Subsequently, candidate solutions, inclusive of their respective derivatives and the wave transformation, are inserted into the DSSH equation. This results in an equation in polynomial form. Terms with equal power are grouped together in the new equation, and their coefficients are set to zero, leading to a system of algebraic equations. Solving this algebraic system facilitates the identification of undetermined parameters within the candidate solutions, thus yielding the solutions for the DSSH equation. Visualization of these solutions is executed through contour plots as well as two- and three-dimensional graphical representations. The contributions of this study are of substantial relevance for subsequent research in nonlinear science. [ABSTRACT FROM AUTHOR]

This article investigates the optical soliton solutions of the Kundu–Mukherjee–Naskar (KMN) equation with the help of the enhanced modified extended tanh method (eMETEM). The equation is crucial for simulating the bending of light beam, rogue waves in the seas, and fiber pulses in optics. Some different kinds of solitons such as singular-periodic, dark and singular for the KMN equation have been successfully obtained by the used method. Utilizing Maple, we confirm that all acquired solutions satisfy the considered equation. We have also analyzed the impact of the parameters graphically in the considered equation. The results shown in the figures reveal that the parameters of the considered equation have an important effect upon soliton dynamics. It is anticipated that the gained solutions and used approach would create remarkable chances for future work in a variety of science areas. [ABSTRACT FROM AUTHOR]

Purpose: In this article, two main subjects are discussed. First, the nonlinear Schrödinger equation (NLSE) with an anti-cubic (AC) nonlinearity equation is examined, which has a great working area, importance and popularity among the study areas of soliton behavior in optical fibers, by using the enhanced modified extended tanh expansion method and a wide range of optical soliton solutions is obtained. Second, the effects of AC parameters on soliton behavior are examined for each obtained soliton type. Methodology: In order to apply the method, the non-linear ordinary differential equation form (NLODE) of the investigated NLSE-AC is obtained by applying the defined wave transformation. Then, with the help of the proposed algorithm for the NLODE form, polynomial form, an algebraic equation system is obtained by setting the coefficients of this form to zero, and the solution of this system is also obtained. After determining the suitable solution set, the optical soliton solution of the investigated problem is obtained with the help of the serial form of the proposed method, a Riccati solution and wave transform. After checking that the solution satisfies the investigated problem, 3D and 2D graphics are obtained for the special parameter values and the necessary comments are made in the relevant sections. Findings: With the proposed method, many optical soliton solutions, such as topological, anti-peaked, combined peaked-bright, combined anti-peaked dark, singular, combined singular-anti peaked, periodic singular, composite kink anti-peaked, kink, periodic and periodic, with different amplitudes are obtained, and 3D and 2D representations have been made. Then, the effect of AC parameters on the soliton behavior in each case has been successfully studied. It has been shown that AC parameters have a significant effect on the soliton behavior, and this effect changes depending on the soliton shape and the parameters. Moreover, providing and maintaining the delicate balance between the soliton shape and the parameters and the interaction of the parameters with each other involves great difficulties. Originality: Although some soliton types of the NLSE-AC equation have been presented for the first time in this study, there is no study in the literature showing the effect of AC parameters on soliton behavior, especially for the NLSE-AC equation. [ABSTRACT FROM AUTHOR]

In this paper, some analytical solutions for a model of dual-core optical fibers governed by a system of coupled non-linear Schrödinger equations (NLSEs) and the effect of the coefficient of the group velocity dispersion term on the considered model are investigated. The group velocity dispersion (GVD) has a important role in the optical wave propagation. The enhanced modified extended tanh expansion method (eMETEM) is successfully implemented to the governing model. The NLSE system is turned into a nonlinear ordinary differential equation (NLODE) via appropriate wave transformations. Supposing that the NLODE has solutions in the form suggested by the method and utilizing the enhanced solutions of the Riccati equation, we gain a nonlinear system of algebraic equations. The solutions of the governing model are obtained after solving the system of algebraic equations. 2D, 3D and contour illustrative figures for the physical interpretation of the attained solutions are presented. Besides, the result of the investigation, which is related to the effect of the coefficient of the group velocity dispersion term, is presented by supporting the various graphical scheme. [ABSTRACT FROM AUTHOR]

In this paper, we aim to derive new soliton solutions of (1+1)- and (2+1)-dimensional generalized Sasa–Satsuma equations via the new Kudryashov method. In optical fiber transmission systems, the Sasa–Satsuma equation describes the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultrafast pulses. The considered equations are encountered in various physical applications such as ultra-short and femto-second pulse propagation in optical fibers and dynamics of deep water waves. So, investigation of the novel solutions of the equations is one of the important topics. We have successfully extracted some soliton solutions for the considered equation. The various graphs of the obtained solutions have been depicted in the figures by selecting appropriate parameters. The singular and bright soliton solutions have been revealed in the figures. All acquired solutions have been confirmed to satisfy the considered equations. The results show that the approach may be used to find exact solutions to various nonlinear evolution equations. The new solutions and the paper results may enrich the understanding of the wave propagation in the optical fibers and may shed light on new studies. [ABSTRACT FROM AUTHOR]

In this paper, we have successfully extracted many analytic solutions for the (1+2)-dimensional Chiral non-linear Schrödinger equation (NLSE) by the enhanced modified extended tanh expansion method (eMETEM). The considered method is a recently enhanced version of the classical modified extended tanh expansion method. So, we have successfully extracted the abundant solutions of the (1+2)-dimensional Chiral NLSE. Using a computer algebra system program, we have verified that all derived solutions satisfy the Chiral NLSE. The plots of some solutions are demonstrated to explain the dynamics of the solutions. It is expected that the results of the paper might be helpful for future works in traveling wave theory. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of soliton solutions for the perturbed Fokas-Lenells (pFL) equation, which has a vital role in optics, using Sardar sub-equation method. The equation models the propagation of ultrashort light pulses in optical fibers. Using appropriate wave transformation, the pFL equation is reduced to a nonlinear ordinary differential equation (NLODE). The solutions of this NLODE equation are assumed to be in the suggested form by the Sardar sub-equation method. Hence, an algebraic equation system is obtained by substituting the trial solution and their necessary derivatives into the NLODE. After finding the unknowns in the system, the soliton solutions of the perturbed Fokas-Lenells equation are extracted. The method produces various kinds of solitons such as dark, periodic, singular periodic, combined bright-dark. To show physical representations of the solitons, 2D, 3D and contour plots of the solutions are demonstrated via computer algebraic systems. It is expected that derived solutions may be useful for future works in various fields of science, especially optics and so, it may contribute to the optic fiber industry. [ABSTRACT FROM AUTHOR]

This paper carries out the analytical optical soliton solutions of perturbed Radhakrishnan–Kundu–Lakshmanan (pRKL) equation with Kerr law nonlinearity using an efficient modified extended tanh expansion method, enhanced with the new Riccati solutions (eMETEM). In this study, we have established robust solutions for the pRKL by using the eMETEM method for the first time. We have focused to construct the effective scheme for the solution of governing model. Bright, dark, combined bright-dark, singular, multiple singular, flat kink-like, breather-like, periodic, different periodic optical solitons have been successfully obtained and confirmed with the help of Maple and Matlab symbolic computation packages. The physical properties of the data have been discussed and presented in 3D, 2D and contour graphics. The results have also been interpreted in the relevant sections. [ABSTRACT FROM AUTHOR]

Some new optical solitons find for the Kudryashov equation (KE) in this study. These solutions are in the form of dark, bright, singular, singular-dark solitons and other solutions with certain conditions. These new solutions may be applied in the demonstration of Kudryashov equation in some better way. Modified integration method, the extended Sinh-Gordon equation expansion method (ShGEEM) is utilized to secure the aforesaid solutions. The results are also verified with the use of Mathematica symbolic programming software. These optical solitons suggest that this method is effective and straight forward compared to other methods and the results are reliable. The obtained solutions are very helpful in the field of optical fibers. [ABSTRACT FROM AUTHOR]

In this research paper, we scrutinize the novel traveling wave solutions and other solutions with conformable, M-truncated and beta fractional derivatives for the nonlinear fractional Hirota–Maccari system. In order to acquire the analytical solutions, the Riccati–Bernoulli sub-ODE technique is implemented. Presented method is the very powerful technique to get the novel exact soliton and other solutions for nonlinear partial equations in sense of both integer and fractional-order derivatives. Mathematical properties of different kinds of fractional derivatives are given in this paper. A comparative approach is presented between the solutions with the fractional derivatives. For the validity of the solutions, the constraints conditions are determined. To illustrate the physical meaning of the presented equation, the 2D and 3D graphs of the acquired solutions are successfully charted by selecting appropriate values of parameters. [ABSTRACT FROM AUTHOR]

This investigation of the current work presents the dispersive concatenation model that integrates the spatio-temporal dispersion and the effect of multiplicative white noise in the Itô sense. The study aims to secure stochastic optical soliton solutions within this framework. To achieve this purpose, we implemented the enhanced Kudryashov technique and the new projective Riccati equations strategy. Initially, the traveling wave transform hypothesis was applied to convert the stochastic model into its nonlinear ordinary differential equation form, encompassing real and imaginary components with emerging the related parametric restrictions. Subsequently, we introduced the enhanced Kudryashov and the new projective Riccati equations techniques successfully employed in analyzing the generated nonlinear ordinary differential equation. By utilizing the appropriate solution sets, which encompass variables with unknown values and necessary transformations, we have derived many stochastic optical soliton-type solutions for the model. Detailed discussions for the dynamics of some selected soliton solutions are presented with the supporting of the 3D and 2D graphs that illustrate the white noise effect on these solitons. • The dispersive concatenation model. • Stochastic optical soliton solutions. • Enhanced Kudryashov technique and the new projective Riccati equations strategy. [ABSTRACT FROM AUTHOR]

The extended generalizing Riccati mapping method (EGRM) is used to solve the derivative nonlinear Schrödinger equation (DNLSe) with the dimensionless shape. This method reveals several optical solitons including traveling wave solutions (TWS). The studied solutions are identified in four different families including the hyperbolic, the rational and the trigonometric functions. Evaluations of the method are presented with graphical results obtained from our solutions. [ABSTRACT FROM AUTHOR]

In this study, two integration techniques are employed to reach optical solitons to the (n + 1) -dimensional nonlinear Schrödinger's equation ((n + 1) -NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented. [ABSTRACT FROM AUTHOR]

A new generalized exponential rational function method (GERFM) is used to acquire some new optical solitons of Radhakrishnan–Kundu–Lakshmanan (RKL) equation with Kerr nonlinearity. This equation is used to model propagation of solitons through an optical fiber. The well-known exponential rational function method is also a special case of the GERFM. The results reveal that the mentioned method is efficient and simple for solving different nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

In this study, we obtained optical soliton solutions of the perturbed nonlinear Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity in the presence of spatio‐temporal dispersion. This equation models the propagation of optical pulses in fiber optic cables. Due to the anti‐cubic nonlinearity, perturbation, and spatio‐temporal dispersion present in the model, it provides more accurate results for high‐speed and long‐distance transmissions. Given the significant developments in the field of optics, studies on complex equations such as this model are of great importance. With the increase in real‐life applications, obtaining solutions to optical equations has become crucial. In this study, we used the improved F‐expansion method to derive the optical soliton solutions for the relevant model. This technique allows for obtaining various solutions through the Jacobi elliptic auxiliary functions it employs. The obtained solutions consist of trigonometric and hyperbolic functions. As a result of the application, 10 solutions were obtained, and 2D and 3D graphics of these solutions are included. These graphs illustrate the motion directions of optical solitons and the effect of the nonlinearity parameter p$$ p $$ and spatio‐temporal dispersion parameter β$$ \beta $$ on soliton behavior. No restrictions were encountered during the study. Finally, the originality of the study lies in the first application of this technique to the relevant model and in examining the effect of the parameters p$$ p $$ and β$$ \beta $$ on this model. [ABSTRACT FROM AUTHOR]

In this paper, optical solitons of higher-order nonlinear Schrödinger equation with Kudryashov's sextic power-law of nonlinear refractive index are investigated via the direct mapping method. The considered model identifies the optical soliton pulse propagation in the optical fibers. Deriving the optical solutions of investigated model such as sextic power is critical but difficult work. The primary aim of this paper is to graphically examine the impact of power-law nonlinearity (pLawNL) and chromatic dispersion (CD) parameters clarifying self-phase modulation (SPM) in the equation on soliton behavior as well as obtaining optical soliton solutions. To according to the used technique, we first used the complex wave transform to generate the nonlinear ordinary differential equation (NLODE) form of the nonlinear Schrödinger equation (NLSE) with Kudryashov's sextic power-law the nonlinear refractive index (SPLawNRI). Then, we were able to produce a system of linear equations in polynomial form by using the approach. Different solution sets including the values of the parameters of the studied equation and the suggested approach were produced by solving the linear system of equations. We acquired the optical soliton solutions of the main equation after inserting the sets and wave transformation into the solution functions suggested by the approach. The constraint conditions for the related solutions were suggested. We proved that the gained solutions satisfied the NLSE with Kudryashov's SPLawNRI under the suggested constraint conditions. We present contour, 3D and 2D depictions in various simulations in figures to comment the obtained solution functions. Besides, we investigate the effects of the power-law nonlinearity parameter that expresses SPM in the main equation and the parameter that are the group velocity dispersion (GVD) or chromatic dispersion (CD) on soliton behavior. The results suggest that the utilized approach is efficient, reliable, and powerful to be readily applied to various NLSEs with higher-order or higher pLawNLs that characterize real-life problems. [ABSTRACT FROM AUTHOR]

In this study, we investigated the time-fractional coupled nonlinear Schrödinger (TF-CNLS) system in conformable fractional sense. TF-CNLS system models the circularly-polarized waves in the optic branch of physics frequently. To obtain optical solitons of the model via new Kudryashov method and Kudryashov auxiliary equation methods have been applied. After implementing the mentioned methods on the model, we obtained bright, singular, W-shaped and bright soliton solutions. According to obtained soliton types, it is clearly seen that the methods are efficient and have ease of use. We depicted the results obtained by 3D and 2D graphs and investigated the wave motion according to the parameter and fractional order changes. We have applied a modulation instability to the TF-CNLS system for the first time. Due to literature research, we propose that this study is innovative and has novel inference. [ABSTRACT FROM AUTHOR]

The importance of efficient analytical methods in solving nonlinear partial differential equations and nonlinear optical differential equations cannot be underestimated. Because of this importance, to solve efficiently above mentioned partial differential equations, a method has been suggested to use the improved Kudryashov and a sub equation form of new extended auxiliary equation methods. In addition the modified form of method has also been given. With this choice, it has been aimed to benefit from the advantages of improved Kudryashov and sub equation of extended auxiliary equation methods at the same time without spending additional processing and time in problem solving, to obtain more solution functions and soliton types offered by the methods. As a first step to implement the proposed method, the nonlinear ordinary differential form (NODE) of the nonlinear partial differential equation has been obtained, the algorithms of the approached methods have been presented and applied to the Biswas–Arshed problem, which is an important equation in optic. Then, the polynomial form of the problem has been obtained, the solution function of the examined problem has been formed by choosing the appropriate sets and their substitutions in the proposed solution functions. It has been checked that the solution functions satisfy the Biswas–Arshed equation and then the graphical representation of the obtained results have been given. The application of the methods has carried out successfully, and both the linear algebraic equations system, the possible solution sets and the solution functions of the main equation, have been obtained seamlessly. It has been observed that both methods can be applied successfully and effectively and more results can be obtained at the same time, without spending an additional procedure and time. It can explicitly seen from both the obtained solution functions and the graphical results that the advantages of both methods can be used at the same time and can be applied to many nonlinear problems. In summary, the originality of this work is that the Biswas–Arshed equation has not been solved with both methods separately before, and it has not been presented in a study showing that both methods can be used together. [ABSTRACT FROM AUTHOR]

This article aims to introduce the generalized stochastic perturbed Schrödinger–Hirota equation, which incorporates multiplicative white noise in the Itô sense. The study focuses on investigating the stochastic optical soliton solutions related to the governing model to understand the characteristics and properties of these soliton solutions. We can achieve this by utilizing the enhanced Kudryashov method and the enhanced direct algebraic approach. The study stands out for its innovative approach to examining the effects of multiplicative white noise on stochastic optical soliton solutions through the lens of the generalized stochastic perturbed Schrödinger–Hirota equation. Utilizing the enhanced Kudryashov method alongside the novel enhanced direct algebraic method, this research effectively identifies and delineates a range of soliton solution types, such as bright, dark, singular, and straddled solitons. This thorough investigation not only underscores the efficacy and efficiency of these methods but also sheds light on the impact of noise on the structural and dynamic properties of soliton solutions, supported by illustrative visualizations. A notable finding is that all solutions derived using the enhanced direct algebraic method feature a nonzero coefficient for the highest-order term of the auxiliary equation. The diversity of solutions obtained through these approaches includes bright, dark, singular, and straddled solitons. Additionally, the study reveals Weierstrass and Jacobi elliptic doubly periodic solutions, which can transition into various soliton types under specific parameter conditions, offering a broader understanding of soliton behavior and properties. [ABSTRACT FROM AUTHOR]

In this paper, the extended Jacobi's elliptic function approach is used to solve the Biswas–Arshed equation in two different types. This method reveals several optical solitons including traveling wave solutions. The found solutions are identified bright, dark, singular optical solitons and Jacobi elliptic function solutions. Reliability of the process is presented with graphical consequence of derived solutions. [ABSTRACT FROM AUTHOR]

This article presents an investigation of soliton solutions for the complex cubic–quintic Ginzburg–Landau equation having anti-cubic law nonlinearity which arises in wave propagation through optical fibers using the enhanced Kudryashov method for the first time. The used method generates all the solutions extracted by classical Kudryashov and new Kudryashov methods at once. This simple yet powerful technique can be applied to a broad range of nonlinear partial differential equations. Applying the method to the Ginzburg–Landau equation, dark, bright, and kink solitons were successfully obtained. Moreover, the effect of the anti-cubic law form, which is the nonlinearity form of the model, on the dynamics of the soliton was examined and it was observed that this form caused a deterioration from a dark soliton to a W-like soliton. Both types of solitons are important in nonlinear systems and are monitored in a variety of physical systems such as optical fibers, Bose–Einstein condensates, and superconductors. This study may have valuable insights into the behavior of soliton solutions of the complex cubic–quintic Ginzburg–Landau equation having anti-cubic law nonlinearity and can contribute to the development of new technologies in nonlinear optics. [ABSTRACT FROM AUTHOR]

In this work, we consider the (2+1)-dimensional Biswas–Milovic equation, which was recently formed. The (1+1)-Biswas–Milovic equation which is a special case of the Schrödinger's equation and it was introduced in 1910. Although there have been many studies on the (1+1) form of the equation, there are hardly any studies on the recently adopted (2+1) and (3+1) forms. Most of the time, it is more meaningful to interpret physical phenomena such as physics, ocean waves, genetics, earthquake, optics depending on the (2+1) and (3+1) dimensional models. Depending on the effect and importance of different nonlinearities forms of self-phase modulation on soliton transmission, obtaining optical soliton solutions under the Kerr and parabolic-law nonlinearities forms of the (2+1)-dimensional Biswas–Milovic equation has been investigated by the new Kudryashov scheme, which was introduced to the literature by N. A. Kudryashov recently. Converting the examined nonlinear partial differential equation to nonlinear ordinary differential form with complex wave transform, obtaining the linear algebraic system by applying the considered method on the transformed form, deriving optical soliton solutions from this system by determining the unknown parameters of the model and method, are the methodologies that form the main framework of the article. Bright, W-like and singular solitons of the analyzed problem were obtained, graphical presentations were made and necessary explanations were made in the relevant sections. The change of the bright soliton to a W-like appearance as an effect of the parabolic law nonlinearity parameter is one of the points obtained and also emphasized in the study. [ABSTRACT FROM AUTHOR]

When it comes to third and higher-order dispersion, the Schrödinger–Hirota equation is one of the main models developed outside the classical NLSE management models for optical soliton transmission. The cubic–quartic Fokas–Lenells equation is also one of the recently developed equations, which has importance in the field of telecommunications regarding optical soliton transmission in the absence of chromatic dispersion. In this study, in order to examine the optical solitons, the Schrödinger–Hirota equation in the presence of the chromatic dispersion and the cubic–quartic Fokas–Lenells equation discarding the chromatic dispersion were investigated. For this intent, by obtaining certain soliton types using the unified Riccati equation expansion method (UREEM), optical soliton solutions were obtained for both models and graphical representations and comments were made. By developing appropriate computer algorithms and applying UREEM in the following ways, symbolic calculation software was made and analytical optical soliton solutions were obtained. Through computer algebra software, we plotted the obtained results via 3D, 2D views and we also illustrated the investigation of wave behavior caused by parameter change on 2D graphics. Different soliton behavior under the parameters effect of the Schrödinger–Hirota equation having chromatic dispersion and the cubic–quartic Fokas-Lenells equation is investigated and the obtained results are reported. [ABSTRACT FROM AUTHOR]

This study aims to examine the optical soliton solutions of the nonlinear Schrödinger form of the (2+1)-Biswas–Milovic equation with Kerr, power and parabolic law nonlinearity. Our method steps are as follows; we have obtained the nonlinear ordinary differential equation (NODE) and constraint relations for each Kerr, power and parabolic law nonlinearity forms of main model by using wave transform. Then we have derived the new Kudryashov method soliton solutions over NODE form and checked the obtained solutions satisfy the nonlinear partial differential equation (NLPDE). Finally, graphic drawings have been created and important comments made on the solution results. The Forms containing Kerr, power and parabolic law nonlinearity of the (2+1)-Biswas–Milovic equation (BME) have been successfully established. The new Kudryashov method (NKM) has been applied and soliton solutions obtained. It is also shown with graphic presentations that the obtained solutions have the basic soliton shapes which are dark, bright and singular. The investigation of the Kerr, power and parabolic law nonlinearity forms of the (2+1)-Biswas–Milovic equation is given in this manuscript for the first time. [ABSTRACT FROM AUTHOR]

The principal purpose of this paper is to examine the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity which governs the propagation of dispersive pulses in optical fibers by proposing and using a direct algebraic form of the enhanced modified extended tanh expansion method for the first time. Our aim is not only restricted to obtaining different and more soliton solutions by proposed method for the first time in this study, but also includes examining the effect of the coefficients of self-steepening and nonlinear dispersion terms to the soliton propagation in the investigated problem. Utilizing a traveling wave transformation, the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity can be transformed into an nonlinear ordinary differential equation (NODE). Then, the NODE is convert into a set of algebraic equations by taking account into the Riccati differential equation. Solving the set of algebraic equations, we acquire the analytical soliton solutions of the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity. In the proposed method, the modified extended tanh function method is enhanced by presenting more solutions of Riccati differential equations with the direct algebraic form, is utilized. The more solutions have been established to the literature with new significant physical properties of the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity. We indicated that the presented method are effective, easily computable, and reliable in solving such nonlinear problems. Moreover, we demonstrate the dynamical behaviors and physical significance of some soliton solutions at appropriate values of parameters. A variety of soliton solutions to the perturbed Schrödinger–Hirota equation with Kerr law non-linearity by the direct algebraic form of enhanced modified extended tanh expansion method have been acquired. These solutions are dark–bright, trigonometric, hyperbolic, periodic, and singular soliton solutions. 3D, contour and 2D plots of some obtained solutions have been demonstrated to interpret the physical meaning of the equation. For some parameter values in the equation, the behavior of soliton solutions has been examined. The constraint conditions are established to confirm the existence of valid solutions. The obtained results can be effective in interpreting the physical meaning of this nonlinear system. We have seen that the proposed direct algebraic form of the enhanced modified extended tanh expansion method is a powerful mathematical technique which can be utilized to acquire the analytical solutions to different complex nonlinear mathematical models. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate analytic soliton solutions of a nonlinear Schrödinger equation (NLSE), including Kudryashov's sextic power-law nonlinearity by introducing different approaches of two efficient analytical methods. The considered equation has been recently introduced by N. A. Kudryashov to describe pulse propagation in optical fibers. The refractive index in the equation comprises six terms, each of the terms containing a power-law component. Applying a wave transformation to the considered NLSE and splitting up the real and imaginary parts, the NLSE is converted to the nonlinear ordinary differential equations (NLODEs). Then, the solutions of NLODEs are considered as suggested in the proposed method and suggested solutions that include some unknown parameters are substituted into the NLODE. An algebraic equations system is acquired by collecting the same power of the unknown function and equating all coefficients to zero. The unknown parameters in the system, and so the solutions of the NLSE, are found by solving the system. In the proposed first method, the modified extended tanh method is enhanced by proposing more solutions. The proposed second method, a different version of auxiliary methods, can remarkably reduce calculations to easily get solutions for the NLSEs with higher-order or power-law nonlinearity. The two proposed methods are successfully applied to the considered NLSE and the abundant solutions of the NLSE are attained. Besides, 2D, 3D and contour graphs are demonstrated in figures for the physical illustrations of the gained solutions. Obtaining the solutions of NLSEs with higher-order or power-law nonlinearity has crucial importance but still challenging work. So, we propose different approaches of two efficient analytical methods, namely, enhanced modified extended tanh expansion method and an auxiliary function method. The derived results imply that the used methods are very efficient, reliable and powerful such that they can be easily implemented to many nonlinear NLSEs with higher-orders or higher power-law nonlinearities that describe real-life phenomena. [ABSTRACT FROM AUTHOR]

We introduce optical soliton solutions of the Kundu–Mukherjee–Naskar (KMN) equation by using the Sardar subequation (SSM) and the new Kudryashov methods (nKM). The KMN equation plays an important role in modeling the fiber pulse in optics, the rogue waves in the oceans and the bending of the light beam. In order to motivate and contribute to researchers working in these fields, we focus on new solutions for the KMN model in fiber pulse transmission by utilizing the Sardar subequation and recently presented New Kudryashov technique. To reach our goal, firstly, the KMN equation has been converted to a nonlinear ordinary differential equation (NODE), then in accordance with the definitions of the proposed methods the solution sets and the solution functions have been obtained. To simulate the new solutions we have obtained and make them more understandable, the topological, anti-topological, periodic,singular and periodic soliton solutions and their properties are presented by 3D and 2D graphics. According to our literature research, these two methods that we are working on have not been applied to the KMN equation before, and we believe that the new solutions we have obtained will be useful to researchers working in modeling in this field. [ABSTRACT FROM AUTHOR]

In this paper, the perturbed Chen–Lee–Liu equation is presented. Sardar subequation method is implemented to retrieve the novel analytical solutions of the given equation. Therefore, some of the optical solitons and other solutions are acquired; besides, constraint conditions are given to guarantee the existence of the obtained solutions. Finally, some of the produced solutions are plotted by the three-dimensional (3D), contour, and two-dimensional (2D) graphs using the suitable values of parameters with the help of the Mathematica in order to indicate the significance of the presented equation. [ABSTRACT FROM AUTHOR]

In this paper, we study the novel exact solutions of the (2 + 1) -dimensional Biswas–Milovic equation for the description of pulse propagation in optical fiber. We successfully constructed some important solutions, such as dark, singular, combined dark-singular soliton, singular periodic wave and rational function solutions, have been analytically obtained using the extended tanh method. These solutions might play an important role in the engineering and physics fields. It is shown that the considered method provide a straightforward and powerful mathematical tool for solving problems in nonlinear optic and other physical phenomena. [ABSTRACT FROM AUTHOR]

This paper studies the perturbed Radhakrishnan–Kundu–Lakshmanan (RKL) equation and its special form, the generalized RKL equation. Kerr law nonlinearity is considered for both equations. The Riccati-Bernoulli sub-ODE technique is implemented to these nonlinear equations so that their optical solitons and complex wave solutions are retrieved. In order to derive a sequence of solutions of considered equations, Bäcklund transformation can be carried out. 3D and 2D graphics of some solutions are depicted for chosen suitable parameters. [ABSTRACT FROM AUTHOR]