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Stability analysis and soliton solutions of the(1+1)-dimensional nonlinear chiral Schrodinger equation in nuclear physics

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Communications in Theoretical Physics 2024年第9期76卷 1-15页

作者： Fazal Badshah Kalim U Tariq ahmet.bekir S M Raza Kazmi Emad Az-Zo'bi School of Electrical and Information Engineering Hubei University of Automotive TechnologyShiyan 442002China Department of Mathematics Mirpur University of Science and TechnologyMirpur-10250(AJK)Pakistan Neighbourhood of Akcaglan Imarli StreetNumber:28/426030EskisehirTurkey Department of Mathematics and Statistics Faculty of ScienceMutah UniversityAlKarak 61710Jordan

The nonlinear Schrodinger equation equation is one of the most important physical models used in optical fiber theory to explain the transmission of an optical *** field of chiral soliton propagation in nuclear physics is very interesting because of its numerous applications in communications and ultra-fast signal routing ***(1+1)-dimensional chiral dynamical structure that describes the soliton behaviour in data transmission is dealt with in this work using a variety of in-depth analytical *** work has applications in particle physics,ionised science,nuclear physics,optics,and other applied mathematical *** are able to develop a variety of solutions to demonstrate the behaviour of solitary wave structures,periodic soliton solutions,chiral soliton solutions,and bell-shaped soliton solutions with the use of applied ***,in order to verify the scientific calculations,the stability analysis for the observed solutions of the governing model is taken into *** addition,the3-dimensional,contour,and 2-dimensional visuals are supplied for a better understanding of the behaviour of the *** employed strategies are dependable,uncomplicated,and effective;yet have not been utilised with the governing model in the literature that is now *** resulting outcomes have impressive applications across a large number of study areas and computational physics phenomena representing real-world *** methods applied in this model are not utilized on the given models in previous literature so we can say that these describe the novelty of the work.

关键词： solitons the nonlinear Schrodinger equation stability analysis chiral solitons exact solutions

Bright and dark soliton solutions for some nonlinear fractional differential equations

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Chinese Physics B 2016年第3期25卷 52-59页

作者： Ozkan Guner ahmet.bekir Cankiri Karatekin University Faculty of Economics and Administrative Sciences Department of International Trade CankiriTurkey Eskisehir Osmangazi University Art-Science Faculty Department of Mathematics-Computer Eskisehir Turkey

In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.

关键词： exact solutions ansatz method space-time fractional modified Benjamin-Bona-Mahoney equa-tion time fractional mKdV equation

Applications of the first integral method to nonlinear evolution equations

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Chinese Physics B 2010年第8期19卷 24-27页

作者： Filiz Tascan ahmet.bekir Eskisehir Osmangazi University Art-Science FacultyDepartment of MathematicsEskisehir-TüRKIYE

In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The obtained results include periodic and solitary wave solutions. The first integral method presents a wider applicability to handling nonlinear wave equations.

关键词： travelling wave solutions first integral method modified Benjamin-Bona-Mahony equa- tion coupled Klein-Gordon equation

Nonlinear dynamical wave structures of Zoomeron equation for population models

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Chinese Physics B 2022年第6期31卷 235-240页

作者： ahmet.bekir Emad H M Zahran Neighbourhood of Akcaglan Imarli StreetNumber:28/426030EskisehirTurkey Departments of Mathematical and Physical Engineering Benha UniversityFaculty of EngineeringShubraEgypt

The nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achieved for the first time in the framwork of the Paul-Painlevéapproach method(PPAM).When the variables appearing in the exact solutions take specific values,the solitary wave solutions will be easily *** realized results prove the efficiency of this technique.

关键词： (2+1)-dimensional non-fractional Zoomeron equation time-fractional biological population model Paul-Painlevéapproach method traveling wave solutions

Exact solutions of nonlinear fractional differential equations by (G'/G)-expansion method

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Chinese Physics B 2013年第11期22卷 140-145页

作者： ahmet.bekir zkan Güner Eskisehir Osmangazi University Art-Science Faculty Department of Mathematics-Computer Dumlup nar University School of Applied Sciences Department of Management Information Systems

In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.

关键词： (G'/G)-expansion method time-fractional Burgers equation fractional-order biological popula-tion model space-time fractional Whitham-Broer-Kaup equations

The Exp-function Method for Some Time-fractional Differential Equations

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IEEE/CAA Journal of Automatica Sinica 2017年第2期4卷 315-321页

作者： ahmet.bekir Ozkan Guner Adem Cevikel Department of Mathematics-computer Eskisehir Osmangazi University Department of International Trade Cankiri Karatekin University Department of Mathematics Education Yildiz Technical University

In this article, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Exp-function method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations in mathematical physics. As a result, some new exact solutions for them are successfully established. It is indicated that the solutions obtained by the Exp-function method are reliable, straightforward and effective method for strongly nonlinear fractional partial equations with modified Riemann-Liouville derivative by Jumarie's. This approach can also be applied to other nonlinear time and space fractional differential equations.

关键词： Exact solution exp-function method fractional differential equation

Singular 1-soliton and Periodic Solutions to the Nonlinear Fisher-Type Equation with Time-Dependent Coefficients

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Communications in Theoretical Physics 2016年第4期65卷 405-409页

作者： Ozkan Guner ahmet.bekir Cankiri Karatekin University Faculty of Economics and Administrative SciencesDepartment of International Trade Eskisehir Osmangazi University Art-Science FacultyDepartment of Mathematics and Computer Science

In this article,we establish exact solutions for the variable-coefficient Fisher-type *** solutions are obtained by the modified sine-cosine method and ansatz *** soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz *** solutions are important for the explanation of some practical physical *** obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients.

关键词： modified sine-cosine method ansatz method the variable-coefficient Fisher-type equation

Exact solutions of some fractional differential equations arising in mathematical biology

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International Journal of Biomathematics 2015年第1期8卷 29-45页

作者： Ozkan Guner ahmet.bekir Department of Management Information Systems School of Applied Sciences Dumlup~nar University Kutahya Turkey Department of Mathematics and Computer Art-Science Faculty Eskisehir Osmangazi University Eskisehir Turkey

In the last decades Exp-function method has been used for solving fractional differential equations. In this paper, we obtain exact solutions of fractional generalized reaction Duff- ing model and nonlinear fractional diffusion-reaction equation. The fractional derivatives are described in the modified Riemann-Liouville sense. The fractional complex trans- form has been suggested to convert fractional-order differential equations with modified Riemann-Liouville derivatives into integer-order differential equations, and the reduced equations can be solved by symbolic computation.

关键词： Fractional partial differential equation exact solutions Exp-function method modified Riemann-Liouville derivative.

Dark Soliton Solutions of Space-Time Fractional Sharma–Tasso–Olver and Potential Kadomtsev–Petviashvili Equations

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Communications in Theoretical Physics 2017年第2期67卷 182-188页

作者： Ozkan Guner Alper Korkmaz ahmet.bekir Cankiri Karatekin University Department of International Trade Cankiri 18200 Turkey ankiri Karatekin University Department of Mathematics Cankiri 18200 Turkey Eskisehir Osniangazi University Department of Mathematics & Computers Eskisehir 26200 Turkey

Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.

关键词： exact solution modified Riemann–Liouville derivative space-time fractional Sharma–Tasso–Olver equation space-time fractional potential Kadomtsev–Petviashvili equation