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The main motivation of the study is to present the (3+1) version of the Biswas–Milovic equation (BME) for the first time and to obtain effective bullet (soliton) solutions. In the literature, it is observed that this equation is generally solved in (1+1) form. The part of the (3+1) dimensional Biswas–Milovic equation containing Kerr law nonlinearity has been solved with new Kudryashov, and the part containing parabolic law nonlinearity solved with the classical Kudryashov method. In this study, we have presented two main models. The model involving Kerr law nonlinearity has been solved with new Kudryashov and one bright bullet obtained. The model containing parabolic law nonlinearity has been solved with classical Kudryashov and one kink bullet obtained. The originality of this study is that the both Kerr law and parabolic law forms of the (3+1) model has never been solved by the methods used in this article. In addition, as well as original bullet solutions, interesting bullet graphs have been obtained with appropriate parameter selections. Moreover the effects of the parameters have been analyzed in detail and explained clearly, with supportive 2d, 3d and contour graphic simulations. [ABSTRACT FROM AUTHOR]

In recent years, depending on the development of models containing highly dispersive nonlinear equations, especially in the field of nonlinear optics, it has been important to obtain the solutions of these equations with analytical methods. This study presents some effective, reliable, and easily applicable solution techniques based on the well-known extended auxiliary equation. Besides, these techniques were applied to the Biswas–Milovic equation. First, in order to achieve the ordinary differential equation structure of the Biswas–Milovic equation, the complex wave transform was given and utilized. Then, the algorithms, constraints of each proposed approach, and key points for their implementation were presented. In addition, the relations and transitivities between the methods are also interpreted. Second, analytical optical soliton solutions were obtained by applying the proposed techniques. Lastly, graphical simulations of optical soliton types represented by some solution functions are made. It has been shown that all of the proposed methods yield effective results in solving the Biswas–Milovic equation and can be used not only for nonlinear evolution equations but also for highly dispersive nonlinear optical equations. It has been observed that the methods have the capacity to be employed easily and do not require tedious calculus and algebraic manipulations. The work in the article has not been presented before. [ABSTRACT FROM AUTHOR]

The aim of this study is to examine the effects of the coefficients of group velocity dispersion, self-frequency shift and self-steepening terms on the optical solitons of the (3+1)-dimensional Sasa–Satsuma equation which is important for modeling many physical events and it has recently been introduced to the literature. To get desired results we have used the solution approach as following. The first step is defining the wave transform and applying it to the nonlinear partial differential equation (NLPDE). Then we have obtained the ordinary differential equation (ODE). Afterwards it is introduced and applied the new Kudryashov method (nKM) and unified Riccati equation expansion method (UREEM) to obtain the algebraic equation system. Finally, by determining the parameters from the solution of algebraic system we have substituted them in the solution function. By using the solution function we have obtained interesting soliton graphics under different parameter values. In addition to the basic solitons of the (3+1)-dimensional Sasa–Satsuma equation (SSE), V-shaped and periodic singular type solitons have also been obtained. The findings of the soliton behaviors under the parameter values effect has not been studied before. The results presented in the article are reported for the first time. • The aim of this study is to examine the effects of the eigenfrequency shift and self-perpendicularity coefficients on the optical solitons of the (3+1) dimensional Sasa–Satsuma equation. • New Kudryashov (nKM) and unified Riccati equation expansion methods have been used. • The most important output of the study is that detailed investigations were made on the effects of the coefficients of group velocity dispersion, self-frequency shift, and self-steepening terms on the soliton behavior, showing that they have a significant impact. • This study will help future research in the optic field of physics. [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]

This manuscript addresses to investigate the optical soliton solution of the Manakov model which governs soliton transmission technology by utilizing the auxiliary equation technique. After obtaining the nonlinear ordinary differential equation form (NODE) of investigated nonlinear partial differential equation problem (NLPDE) with the complex wave transform (cWT), the serial form is suggested in accordance with the utilized auxiliary method, and after written in the NODE form, the linear algebraic system is formed and by aid of the any symbolic calculation package the unknown parameters are obtained. In order to gain the soliton solutions, the proposed series form, the solution functions of the method, and the cWT are brought together and it is checked that the obtained solutions satisfy the main equation. By considering the functions that satisfy the main equation as solutions, graphical presentations are made and interpreted in order to better understand the obtained results. By applying the effective auxiliary equation method, optical soliton pulse solutions such as bright, singular, V-shaped, periodic singular, periodic bright, periodic bright–dark have been obtained, and it has been shown that the method can be applied effectively for such equations. The auxiliary equation method has not been applied to the Manakov model and the V-shaped, periodic singular, periodic bright soliton pulse solutions have not been reported before. [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]

In the last decades, many researchers have performed their best in order to find the solution of the nonlinear evolution equations, nonlinear partial differential equations (NLPDEs), fractional nonlinear partial differential equations and nonlinear optical models by using Kudryashov methods, which have various forms. However, most researchers have used different methods under the same name or applied the same method under the different names. This situation has created confusion for researchers and readers, such as choosing the appropriate method, algorithm and the right article title. In order to eliminate this problem and to clarify the methods, we have conducted rigorous research and wrote a certain standard in this field by bringing together the Kudryashov methods, which are widely used under different names in the literature. Besides, it has been aimed to give the general algorithm of the methods, to make some addendums on the methods and to present new approaches to these methods for the researchers. We strongly believe that the study will be of great benefit not only for those who are interested in nonlinear evolution problems, but also for studies in the field optics. Regarding the methods, first of all, the articles of the researchers who suggested the methods and the studies of the respected researchers in this field have been examined and tried to gather under one framework and give a general name with appropriate algorithm for each Kudryashov method. The algorithms and solution functions of each method have been checked on the related Riccati and Bernoulli equations with different softwares (Mathematica, Maple, Matlab, etc.), and confirmed every results carefully. Afterwards, all methods have been applied on (2+1)-dimensional Zoomeron equation for the global test purpose. With the usual standard approach, the nonlinear partial differential form of Zoomeron equation has been transformed into the nonlinear ordinary differential (NODE) form by applying the wave transformation, then each method applied to the NODE form of Zoomeron equation. After these operations, we have obtained a system of linear algebraic equations and their appropriate solutions. By obtaining the appropriate solution sets, the soliton solutions of the Zoomeron equation have been constructed and some selected graphical presentations given. The results have been obtained from the applications that applied on the Zoomeron equation via Kudryashov methods shows us they can be used widely and effectively in the solution of not only nonlinear evolution problems, but also highly dispersive and higher order nonlinear partial differential equations. It has been seen that all the applied Kudryashov methods give effective results. Besides, controlling and using the parameters in the Kudryashov methods play important role, especially obtaining the effective and desired solution sets. Based on our detailed research, we could not find any summative study in this area like this one. In addition to all these, some of the approaches and addendums have been presented for the first time in this paper. Besides, (2+1)-dimensional Zoomeron equation has also not been previously solved by some of these methods. It is thought that this study will be used as a reference by many researchers in the future and it will be of great benefit to researchers. [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]

The aim of this study is to introduce the stochastic dispersive Schrödinger–Hirota equation with parabolic law nonlinearity (SHEPL) with multiplicative white noise via Ito calculus and investigate its stochastic optical soliton solutions. For this purpose, we used unified Riccati equation expansion (UREEM) and a sub-version of an auxiliary methods to construct analytical solutions. Firstly, we implemented traveling wave transform into SHEPL with multiplicative white noise via Ito calculus and constructed imaginary and real parts of its nonlinear ordinary differential equation (NODE) form. Then, we presented solution algorithms of UREEM and a sub-version of an auxiliary methods and successfully implemented to obtained NODE. We created analytical solutions of SHEPL with using the appropriate solution sets which involve unknown parameters and necessary transformations. Then we presented graphical representations of these solution functions by investigating the noise effect on the soliton structure and presented the gained results. We proposed the stochastic SHEPL equation for the first time in this article. We obtained stochastic optical soliton solutions, reflected their graphical representations and also observed effect of noise factor on the obtained soliton structure. The stochastic model of SHEPL has not been studied and the results have not been reported. • The aim of this study is to introduce the stochastic dispersive Schrödinger–Hirota equation with parabolic law nonlinearity (SHEPL) with multiplicative white noise via Ito calculus and investigate its stochastic optical soliton solutions. • We used unified Riccati equation expansion (UREEM) and a sub-version of auxiliary methods to construct analytical solutions. • The stochastic model of SHEPL has not been studied before the presented results have not been reported. [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 have searched for optical solutions of Kaup–Newell equation (KNE) used in nonlinear optical and plasma physics, which have a very important role in the class of derivative nonlinear Schrödinger equations (dNLSEs). To obtain exact wave solutions of the proposed model, two analytical techniques, recently presented as new Kudryashov's method and the generalized projective Riccati equations method (GPREM) have been applied for the first time. These two methods are based on traveling wave transformation and homogeneous balance principles. The presented nonlinear partial differential equation (NLPDE) has been converted to ordinary differential equation (ODE) using traveling wave transformation. Thus, new analytical solutions have been obtained by applying the proposed methods. The new solitons and other traveling wave solutions acquired will be a motivation to researchers working in engineering and applied physics. Various constraints have been used to ensure the validity of the obtained solutions and to get the most appropriate solutions. To illustrate the physical phenomena of this model, 2D, 3D and contour plots of some derived solutions have been depicted with explanatory graphics. [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]

The modified extended tanh expansion method is applied to the perturbed Chen–Lee–Liu equation where the perturbation terms are with full nonlinearity. This method contributes a variety of optical soliton solutions including dark, singular, dark-singular soliton, singular periodic waves and rational function solutions to the perturbed Chen–Lee–Liu equation. The constraint conditions that validate the existence of the reported soliton solutions are acquired. The 2D, 3D, and the contour graphs of some of the obtained solutions are plotted. [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]