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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 study examines for the first time the adapted parabolic law nonlinearity form of (2+1)-dimensional Davey-Stewartson system, an important equation modeling the surface water wave packets with finite depth. For the first time, we will investigate the parabolic law nonlinearity form. Not only is this a significant aspect, but we will also explore it with various parameter values to see its impact on soliton dynamics. In order to transform the nonlinear partial differential equation into a form for which the analytical method can be applied, the ordinary differential equation structure obtained by first applying wave transformation. In the following stage, we implement the new Kudryashov method and sinh-Gordon equation expansion techniques to retrieve bright, dark, singular, and different types of kink solitons. The effect of parabolic law nonlinearity parameters on the obtained soliton types has also been examined. We illustrate the 3D and 2D graphs of some of the obtained solutions to gain a physical perspective. The study will contribute to the literature in terms of the form of the examined problem, its content and results, and the effectiveness of the applied methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a numerical technique for solving the Cauchy non-homogeneous time-fractional diffusion-wave equation with the Caputo derivative operator. The key idea behind our approach is to employ the roots of shifted Chebyshev polynomials to collocate the problem in the time dimension. By introducing certain functions to homogenize the resulting system of ordinary differential equations, we obtain an approximate solution to the problem. To assess the reliability of our method, we conduct a thorough comparison with existing numerical techniques available in the literature. Through extensive experimentation, we demonstrate the effectiveness and accuracy of our proposed technique. Notably, the results highlight the efficiency and precision of our method in approximating solutions for the considered problem. Furthermore, we investigate the convergence of our method and provide theoretical insights into its performance. Our findings support the validity and robustness of the proposed approach. Overall, this paper contributes a valuable numerical tool for addressing the Cauchy non-homogeneous time-fractional diffusion-wave equation, offering enhanced efficiency and accuracy compared to existing methods. [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]

In this manuscript, the density-dependent space-time fractional reaction–diffusion equation in the sense of conformable and M-truncated derivatives (CMD) is presented. Through fractional transformation, these nonlinear fractional equations can be converted into nonlinear ordinary differential equations (NLPDEs). Besides, with the help of the Riccati–Bernoulli sub-ODE method (RBM), new exact solutions for these nonlinear fractional equations are produced. In order to construct the comparative analysis between different type fractional derivatives, graphical representations are demonstrated for chosen values of unknown parameters. [ABSTRACT FROM AUTHOR]

In this research paper, we take into account the (2 + 1)-dimensional Kadomtsev–Petviashvili equation which is important in the soliton theory of nonlinear physics. To get the desired soliton solutions, the modified F-expansion method using the Riccati equation which has many solution functions, as well as the modified generalized Kudryashov's method, had been effectively implemented. One of the reasons for the preference of the methods is that the proposed methods have been widely used before and they have not been applied to this problem. First, the wave transform is applied to the considered nonlinear partial differential equation (NLPDE), the nonlinear ordinary differential equation (NODE) form and the balancing constant are determined. The next step is to use the auxiliary equation depending on the proposed method to find the solution of the NODE form and to obtain the linear algebraic equation system. The solution of this system gives different solution sets for unknown parameter values. Then, soliton solution functions are constructed by using the suitable solution sets. After testing and confirming that the obtained solution functions satisfy the main equation, the three- and two-dimensional illustrations are depicted. [ABSTRACT FROM AUTHOR]

Purpose: This study includes the examination of the cases where the (1 + 1) -dimensional chiral nonlinear Schrödinger equation also has Bohm potential. This review is not to obtain different soliton solutions for both cases but to obtain a certain type of soliton and to observe the effect of the problem parameters. By using the modified new Kudryashovs scheme. This observation also includes how the soliton behavior is effective by comparing the (1 + 1) -dimensional chiral nonlinear Schrödinger equation (C-NLSE) and (1 + 1) -dimensional chiral nonlinear Schrödinger equation with Bohm potential (C-NLSE-BP), especially by examining the Bohm potential parameter. Methodology: In order to apply the proposed analytical method which is the modified Kudryasovs scheme (m-NKM), as in many studies, the nonlinear partial ordinary differential equation (NLPDE) is first converted into nonlinear ordinary differential equation form (NLODE) by using wave transform. Then, in order to determine which degree the solution function to be proposed will be, the balancing constant is calculated. The next step is to determine the unknown parameters of the problem by applying the m-NKM on NODE, obtaining solution sets, and combine the solution of the Riccati equation, which is the basis of the method, with the proposed solution function and wave transform. Obtaining the optical solution by providing the main NLPDE is the next step that follows this stage. The final stage is the graphical analysis and interpretation of the parameter effect for both problems using the obtained solution function. Findings: The examination of the case with and without Bohm potential was carried out on the behavior of the bright soliton shape, which is one of the basic soliton shapes that many effects can be clearly studied on it. It was successfully shown that both equation parameters and the Bohm potential had a significant effect on the soliton behavior, graphical presentations were made and interpreted in detail. Originality: Such an examination has not been studied before in the literature for the investigated equations. [ABSTRACT FROM AUTHOR]

The aim of this study is to peruse the dispersive Schrödinger–Hirota equation (SH equation) with parabolic law linearity to get optical soliton solutions by utilizing the generalized Kudryashov method (GKM). Firstly, we introduced the solution algorithm of GKM. Then, we substituted the traveling wave transform to dispersive SH equation with parabolic law and gained nonlinear ordinary differential equation (NODE) form of real and imaginary parts. We successfully applied GKM to the NODE form of dispersive SH equation and obtained the appropriate solution sets. Using these sets, the solution of differential equation and necessary transformations, we created the analytical solution functions of dispersive SH equation and demonstrated the graphical simulations. Optical soliton solutions were obtained, graphical representations were made and interpreted, at the same time, it was observed that some parameters had an effect on the soliton behavior. The parabolic law form of the examined model has not been studied, and the obtained results have not been reported. [ABSTRACT FROM AUTHOR]

In this article, the aim was to obtain kink soliton solutions of the (2+1)-dimensional integro-differential Jaulent–Miodek equation (IDJME), which is a prominent model related to energy-dependent Schrödinger potential and is used in fluid dynamics, condensed matter physics, optics and many engineering systems. The IDJME is created depending on the parameters and with constant coefficients, and two efficient methods, the generalized Kudryashov and a sub-version of an auxiliary equation method, were applied for the first time. Initially, the traveling wave transform, which comes from Lie symmetry infinitesimals ∂ ∂ x , ∂ ∂ y and ∂ ∂ t , was applied, and a nonlinear ordinary differential equation (NODE) form was derived. In order to make physical interpretations, appropriate solution sets and soliton solutions were obtained by performing systematic operations in line with the algorithm of the proposed methods. Then, 3D, 2D and contour simulations were made. Interpretations of different kink soliton solutions were made by obtaining results that are consistent with previous studies in the literature. The obtained results contribute to the studies in this field, though the contribution is small. [ABSTRACT FROM AUTHOR]

This article investigates the optical soliton solutions of the time-fractional Biswas–Arshed (BA) equation, which is a new model for soliton transmission through optical fibers where the eigen-phase modulation is negligible and thus removed. We have studied both models including M-truncated or beta derivative operators. Firstly, the time-fractional BA equations have been transformed into a nonlinear ordinary differential equation using appropriate wave transformations. The singular, singular-periodic, and dark soliton solutions have been derived using the extended rational sine–cosine and sinh–cosh techniques have been applied and the existing conditions for the obtained solutions have been introduced. Utilizing a computer algebraic system, we have verified that all of the derived solutions satisfy the fractional Biswas–Arshed equation. Additionally, we have compared the results for the beta and M-truncated derivatives and have examined how the equation's parameters affect the amplitude of the solitons in 2D and 3D graphical demonstrations. The attained solutions may aid in the comprehension of wave propagation in optical fibers and may contribute to the telecommunication sector. [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]

In this article, we obtain new fractional solutions of the general class of non-Fuchsian differential equations by using discrete fractional nabla operator ∇ η (0 < η < 1) . This operator is applied to homogeneous and nonhomogeneous linear ordinary differential equations. Thus, we obtain new solutions in fractional forms by a newly developed method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the spread of a non-fatal disease in a population is solved by using the Hermite collocation method. Mathematical modeling of the problem corresponds to a three-dimensional system of nonlinear ODEs. The presented scheme reduces the problem to a nonlinear algebraic equation system by expanding the approximate solutions by using Hermite polynomials with unknown coefficients. These coefficients of the Hermite polynomials are computed by using the matrix operations of derivatives together with the collocation method. Maple software is used to carry out the computations. In addition, comparison of our method with the Homotopy perturbation method (HPM) and Laplece-Adomian decomposition method (LADM) proves accuracy of solution. [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, we propose a new approach for solving boundary value problems a differential equation with retarded argument:x″(t)+a(t)x(t−τ(t))=f(t),x(t)=ϕ(t)(λ0⩽t⩽0), x(T)=xT ,where 0⩽t⩽T and a(t), f(t), τ(t)⩾0(0⩽t⩽T) and ϕ(t)(λ0⩽t⩽0) are known continuous functions. A differential equation with retarded argument is computed by converting the obtained series solution into padé series. First we calculate power series of the given equation system then transform it into padé (approximants) series form, which give an arbitrary order for solving differential equation numerically. [Copyright &y& Elsevier]

The aim of this paper is to present an efficient numerical procedure for solving boundary value problems for a differential equation with retarded argument:x′′(t)+a(t)x(t−τ(t))=f(t),x(t)=ϕ(t) (λ0&les;t&les;0), x(T)=xT,where 0&les;t&les;T and a(t),f(t),τ(t)&ges;0 (0&les;t&les;T) and ϕ(t) (λ0&les;t&les;0) are known continuous functions. A differential equation with retarded argument is computed by converting the obtained series solution into Pade´ (approximants) series. First we calculate power series of the given equation system then transform it into Pade´ (approximants) series form, which give an arbitrary order for solving differential equation numerically. [Copyright &y& Elsevier]

The aim of this paper is to present an efficient numerical procedure for solving boundary value problems for a differential equation with retarded argument:x″(t)+a(t)x(t−τ(t))=f(t)x(t)=ϕ(t) (λ0&les;t&les;0), x(T)=xT,where 0&les;t&les;T and a(t),f(t),τ(t)&ges;0 (0&les;t&les;T) and ϕ(t) (λ0&les;t&les;0) are known continuous functions. A differential equation with retarded argument is computed by converting the obtained series solution into Pade´ (approximants) series. First we calculate power series of the given equation system then transform it into Pade´ (approximants) series form, which give an arbitrary order for solving differential equation numerically. [Copyright &y& Elsevier]

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]

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]