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    Examination of optical soliton solutions for the perturbed Schrödinger-Hirota equation with anti-cubic law in the presence of spatiotemporal dispersion
    (Springer Heidelberg, 2024) Durmus, Selvi Altun; Ozdemir, Neslihan; Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa
    In the current paper, the perturbed Schr & ouml;dinger-Hirota equation having anti-cubic nonlinearity is analyzed with the aid of the new Kudryashov scheme. What distinguishes this article from other articles is that it not only attains multifold analytical solutions to the underresearched model but also verifies the impact of the anti-cubic law media on soliton attitude for the first time. The algorithmic rules and solution functions of the presented method have been controlled with symbolic algebraic software, and every outcome has been approved attentively. Then, the given method has been implemented on the model under consideration for the collective test objective. With the conventional norm approximation, the nonlinear partial differential structure of the model under consideration has been turned into the ordinary differential structure by performing the wave transmutation, and then the presented technique has been implemented into the ordinary differential structure of the proposed model. After this process, we have acquired a system of linear algebraic equations and their convenient solutions. Afterward, by attaining the proper solution sets, the soliton solutions of the given model, such as bright, W-shape-like, and dark soliton forms, have been arranged, and some chosen diagrammatic views have been presented.
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    Investigation of optical soliton solutions of higher-order nonlinear Schrödinger equation having Kudryashov nonlinear refractive index
    (Elsevier GmbH, 2023) Ozisik, Muslum; Secer, Aydin; Bayram, Mustafa; Cinar, Melih; Ozdemir, Neslihan; Esen, Handenur; Onder, Ismail
    Purpose: 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. Methodology: 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. Findings: 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. Originality: 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. © 2023 Elsevier GmbH
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    Obtaining the soliton solutions of local M-fractional magneto-electro-elastic media
    (Cell Press, 2023) Ozdemir, Neslihan; Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa
    In this research paper, the generalized projective Riccati equations method (GPREM) is applied successfully to procure the soliton solutions of the local M-fractional longitudinal wave equation (LWE) arising in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic circular rod (MEECR). Applying a wave transformation to the local M-fractional LWE, the equation can be turned into a set of algebraic equations. Solving the algebraic equation system, we procure the soliton solutions of the local M-fractional LWE. Both the obtained solution functions in the study and the graphical simulations depicted for these functions. It will assist researchers working in this field in the physical interpretation of this equation. Moreover, the reported solutions propose a rich platform to examine the local M-fractional LWE.
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    Optical soliton solutions of the nonlinear Schrodinger equation in the presence of chromatic dispersion with cubic-quintic-septic-nonicnonlinearities
    (Iop Publishing Ltd, 2023) Ozdemir, Neslihan; Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa
    In this study, one of our main subjects is the examination of optical solitons of the nonlinear Schrodinger equation having cubic-quintic-septic-nonic nonlinearities via the modified F-expansion method. The other subject is also the analysis of the impacts of some parameters in the model on the soliton shape, which is examined for the first time in this study. According to the modified F-expansion method, we select the suitable transformation to gain the nonlinear ordinary differential equation for the nonlinear Schrodinger equation having cubic-quintic-septic-nonic nonlinearities in the first stage. Then, we get a system consisting of linear equations in polynomial form with the aid of the modified F-expansion method. Various solution sets consisting of the parameters of the nonlinear Schrodinger equation having cubic-quintic-septic-nonic nonlinearities are achieved. Inserting the selected sets and transformations into the serial form of the presented method and utilizing the solutions of the auxiliary equation in the presented method, the optical soliton solutions of the model are derived. Furthermore, varied optical soliton solutions, such as anti-kink, singular, and bright, are achieved, and 3D and 2D projections of the generated soliton solutions have been illustrated. The impact of some parameters on each soliton behavior has also been examined. It is found that these parameters have a significant impact on the soliton structure.
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    Optical solitons for the dispersive Schrodinger-Hirota equation in the presence of spatio-temporal dispersion with parabolic law
    (Springer Heidelberg, 2023) Ozdemir, Neslihan; Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa
    This research article holds two main purposes. The first purpose is obtaining the optical soliton solutions of the (1 + 1)-dimensional dispersive Schrdinger-Hirota equation in the presence of spatio-temporal dispersion with parabolic law nonlinearity. The second is scrutinizing the impact of the parameters. We utilized the new Kudryashov scheme which is the recent effective, efficient, and easily applicable technique. Performing the wave transformation the nonlinear ordinary differential form (NLODF) is gained. Then utilizing the new Kudryashov method the polynomial structure and its solution sets are derived. Selecting the appropriate solution set, establishing the solution function, providing the main equation, linear modulation stability analysis, and graphical presentations in 3D, and 2D are the issues performed in the remaining parts of the article.
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    Soliton and other solutions of the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation with conformable derivative
    (Iop Publishing Ltd, 2023) Ozdemir, Neslihan; Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa
    In this scientific research article, we consider the (2 + 1)- dimensional Date-Jimbo-Kashiwara-Miwa equation with conformable derivative (C-DJKME), a water wave model with low surface tension and long wavelengths with weakly nonlinear restoring forces and frequency dispersion. Since the solutions of C-DJKME constitute the basis and model of many physical phenomena, we see many original studies with interesting physical properties in the literature. In our research, to acquire exact and soliton solutions of the C-DJKME, the Sardar Subequation method and the new Kudryashov method are employed for the first time. We have shown that these two methods are very effective, easily applicable, and reliable in solving such nonlinear problems. Finally, the graphs of some solutions are depicted at appropriate values of parameters. The impact of the fractional parameter on the acquired solutions is also demonstrated through 2D plots.
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    Soliton solutions of Heisenberg spin chain equation with parabolic law nonlinearity
    (Springer, 2023) Altun, Selvi; Ozdemir, Neslihan; Ozisik, Muslum; Secer, Aydin; Bayram, Mustafa
    In this article, we presented and investigated a model of the (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation with parabolic law nonlinearity, for the first time. This study intends on two main elements. The first is to construct the parabolic law nonlinearity form of the HFSC model, and the second is to peruse the effect of this form on the soliton wave behavior. Two different analytical techniques, which are a subversion of the new extended auxiliary equation method and the improved generalized Kudryashov method (iGKM), are applicated to construct the soliton solutions of investigated HFSC form. With the help of these methods, bright, singular, and kink soliton forms have been obtained and their characteristics have been depicted by 2D and 3D diagrams. In accordance with our litterateur investigation, the subject of the study and the results obtained have not been reported before and we can say that the results we have attained will be a guide for researchers who want to study in this field.