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    Bright soliton of the third-order nonlinear Schrödinger equation with power law of self-phase modulation in the absence of chromatic dispersion
    (Springer, 2024) Durmus, Selvi Altun; Ozdemir, Neslihan; Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa
    In this article, we are interested in two principal topics. First, the bright optical soliton solutions of the third-order (1+1)-nonlinear Schrodinger equation including power law nonlinearity with inter-modal and spatio-temporal dispersions are perused by taking advantage of the new Kudryashov method. Second, the impacts of power law nonlinearity parameters on soliton attitude are investigated for acquired bright soliton form. With the proposed technique, the bright optical soliton solution is acquired, and 3D, contour, and 2D plots are depicted. Then, the impact of power law nonlinearity parameters on the soliton attitude has been successfully demonstrated. As is clear from this perusal power law parameters have an important impact on the soliton attitude, and this impact alters based on the soliton form. As regards our investigation, this form of the equation has not been studied with the power law nonlinearity in the absence of the chromatic dispersion for nonlinear models and the proposed method has not been applied the introduced equation before. It is expected that the consequences which are acquired in this study will shed light on the studies in this field.
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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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    Investigation of soliton solutions to the Peyrard-Bishop-Deoxyribo-Nucleic-Acid dynamic model with beta-derivative
    (World Scientific Publ Co Pte Ltd, 2024) Secer, Aydin; Ozisik, Muslum; Bayram, Mustafa; Ozdemir, Neslihan; Cinar, Melih
    This study purposes to extract some fractional analytical solutions of the Peyrard-Bishop-Deoxyribo-Nucleic-Acid (beta-PBDNA) dynamic model with the beta-derivative by the unified Riccati equation expansion method (UREEM). Furthermore, we examine the role of various parameters of the fractional model on the soliton dynamic. The research focuses on computational biophysics and materials science, examining the impact of various parameters on the fractional model. This paper contributes to understanding soliton solutions and the beta-PBDNA dynamic model, demonstrating the applicability of the UREEM method to various fractional models. Some soliton solutions of the model are successfully generated by applying the UREEM. Implementing the UREEM, we take a fractional wave transformation to convert the model into a nonlinear ordinary differential equation. So, a linear equation system is generated. After the system is solved, the soliton solutions are gained for the appropriate solution sets. Finally, 3D, 2D and contour graphs of diverse solutions are depicted at suitable values of parameters. In addition, this paper presents 3D, 2D and contour graphs of various solutions with suitable parameter values. The results are beneficial for interpreting the model in future work and confirm that UREEM is effectively applicable to diverse fractional models, coupled with a comprehensive graphical analysis of how different parameters influence these solutions.
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    Nonlinear complex generalized zakharov dynamical system inconformal sense utilizing new kudryashov method
    (Iop Publishing Ltd, 2024) Secer, Aydin; Bayram, Mustafa; Ozdemir, Neslihan; Onder, Ismail; Esen, Handenur; Cinar, Melih; Aydin, Huseyin
    We take into account the nonlinear complex generalized Zakharov dynamical system which models the spread of the Langmuir waves in ionized plasma, in the conformal sense in this manuscript. Fractional wave transformation is enforced to convert the nonlinear fractional system to a nonlinear ordinary differential equation system. The new Kudryashov method which was recently introduced and is an efficient method, is implemented to the presented equation to acquire analytical solutions. The required constraint conditions are offered to ensure the validity of the obtained solutions. To analyze the physical interpretations for some of the produced solutions, we illustrate some graphical representations. We derive the bright and singular solitons. Furthermore, 2D views of the behavior of the solitons are represented to investigate the effect of the values of the parameters in the proposed model and fractional parameters. Also, the modulation instability of the model is investigated to ensure the obtained results are stable.
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    Novel soliton solutions of Sasa-Satsuma model with local derivative via an analytical technique
    (Aip Publishing, 2022) Ozdemir, Neslihan; Esen, Handenur; Secer, Aydin; Bayram, Mustafa
    In this research article, the Sardar subequation method is used to retrieve new analytical solutions to the space-time local derivative Sasa-Satsuma equation with Atangana's conformable derivative, which defines short pulse propagation in an optical fiber area. This equation is the integrable extension of the nonlinear Schrodinger equation. First, the equation is transformed into an ordinary differential equation utilizing traveling wave transformation. Then, novel different type soliton solutions are acquired using the Sardar subequation approach. The produced soliton solutions play an essential role for scientists in interpreting the physical phenomenon of this equation. Finally, the graphs of some solutions are depicted at appropriate values of parameters. The achieved results show the simplicity, reliability, and potentiality of the proposed method.& nbsp;& nbsp;Published under an exclusive license by AIP Publishing.
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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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    On the soliton solutions to the density-dependent space time fractional reaction-diffusion equation with conformable and M-truncated derivatives
    (Springer, 2023) Esen, Handenur; Ozdemir, Neslihan; Secer, Aydin; Bayram, Mustafa; Sulaiman, Tukur Abdulkadir; Ahmad, Hijaz; Yusuf, Abdullahi
    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.
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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 and other solutions to the Hirota-Maccari system with conformable, M-truncated and beta derivatives
    (World Scientific Publ Co Pte Ltd, 2022) Ozdemir, Neslihan; Esen, Handenur; Secer, Aydin; Bayram, Mustafa; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadir
    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.
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    Optical solitons for the Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion
    (Iop Publishing Ltd, 2023) Ozdemir, Neslihan
    For the first time, the optical soliton solutions of the (1 + 1)-dimensional Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion are intended to be analyzed in detail. To attain this purpose, the new Kudryashov and the Kudryashov auxiliary equation technique are successfully implemented. Moreover, the impacts of model parameters on the soliton dynamics are scrutinized. The complex wave transformation is utilized to get the nonlinear ordinary differential equation form and to generate soliton solutions, the presented methods are performed. Finally, various graphical illustrations were derived and detailed comments were added on the solution results. The new Kudryashov approach and the Kudryashov auxiliary equation technique have been successfully performed and soliton solutions obtained. W-shape soliton was acquired with the new Kudryashov approach and the bright soliton was acquired with the Kudryashov auxiliary equation technique. Furthermore, diverse graphic descriptions that the resulting soliton solutions are obtained, and 2D graphs are presented and commented on. Since the Biswas-Milovic equation, which is the subject of much research, has an important role in nonlinear optics, different forms of the Biswas-Milovic equation are developed in the literature. The model in the presence of spatio-temporal dispersion was presented and scrutinized for the first time.
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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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    Solitary wave solutions of chiral nonlinear Schrodinger equations
    (World Scientific Publ Co Pte Ltd, 2021) Esen, Handenur; Ozdemir, Neslihan; Secer, Aydin; Bayram, Mustafa; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi
    This paper presents the (1+1)-dimensional chiral nonlinear Schrodinger equation (1DCNLSE) and (2+1)-dimensional chiral nonlinear Schrodinger equation (2DCNLSE) that define the edge states of the fractional quantum hall effect. In this paper, we implement the Riccati-Bernoulli sub-ODE method in reporting the solutions of these two nonlinear physical models. As a result of this, some singular periodic waves, dark and singular optical soliton solutions are generated for these models. Some of the acquired solutions are illustrated by three-dimensional (3D) and two-dimensional (2D) graphs utilizing suitable values of the parameters with the help of the MAPLE software to demonstrate the importance in the real-world of the presented equations.
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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.