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    Computational method to solve Davey-Stewartson model and Maccari’s system
    (YILDIZ TECHNICAL UNIV, YILDIZ CAMPUS, BESIKTAS, ISTANBUL 34349, Turkiye, 2024) Esen, Handenur; Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa
    In this article, Computer algebra systems and the Riccati-Bernoulli sub-ODE method are efficiently utilized to solve Davey-Stewartson and Maccari’s systems. We successfully obtained the set of new exact solutions for these systems using the computer algebra MAPLE system. For the validity of acquired solutions, the constraint conditions are given. To investigate the behavior of these solutions, graphical representations of the derived solutions are provided under suitable parameter values.
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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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    Nonlinear complex generalized zakharov dynamical system inconformal sense utilizing new kudryashov method
    (Iop Publishing Ltd, 2024) Seçer, Aydın; Bayram, Mustafa; Özdemir, Neslihan; Önder, İsmail; Esen, Handenur; Çınar, Melih; Aydın, Hüseyin
    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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    On the investigation of optical soliton solutions of cubic-quartic Fokas-Lenells and Schrodinger-Hirota equations
    (ELSEVIER GMBH, HACKERBRUCKE 6, 80335 MUNICH, GERMANY, 2023) Özışık, Müslüm; Önder, İsmail; Esen, Handenur; Çınar, Melih; Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa
    Purpose: 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. Methodology: By developing appropriate computer algorithms and applying UREEM in the following ways, symbolic calculation software was made and analytical optical soliton solutions were obtained. Findings: 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. Originality: 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.
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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 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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    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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    Traveling wave structures of some fourth-order nonlinear partial differential equations
    (ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS, 2023) Esen, Handenur; Özdemir, Neslihan; Seçer, Aydın; Bayram, Mustafa
    This study presents a large family of the traveling wave solutions to the two fourth-order nonlinear partial differential equations utilizing the Riccati-Bernoulli sub-ODE method. In this method, utilizing a traveling wave transformation with the aid of the Riccati-Bernoulli equation, the fourth-order equation can be transformed into a set of algebraic equations. Solving the set of algebraic equations, we acquire the novel exact solutions of the integrable fourth-order equations presented in this research paper. The physical interpretation of the nonlinear models are also detailed through the exact solutions, which demonstrate the effectiveness of the presented method.The Bäcklund transformation can produce an infinite sequence of solutions of the given two fourth-order nonlinear partial differential equations. Finally, 3D graphs of some derived solutions in this paper are depicted through suitable parameter values.