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Stability analysis and soliton solutions of the(1+1)-dimensional nonlinear chiral Schr?dinger 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 Technology Department of Mathematics Mirpur University of Science and Technology Neighbourhood of Akcaglan Department of Mathematics and Statistics Faculty of Science Mutah University

The nonlinear Schr?dinger equation equation is one of the most important physical models used in optical fiber theory to explain the transmission of an optical soliton. The field of chiral soliton propagation in nuclear physics is very interesting because of its numerous applications in communications and ultra-fast signal routing systems. The (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 techniques. This work has applications in particle physics, ionised science, nuclear physics, optics, and other applied mathematical sciences. We 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 techniques. Moreover, in order to verify the scientific calculations, the stability analysis for the observed solutions of the governing model is taken into consideration. In addition, the3-dimensional, contour, and 2-dimensional visuals are supplied for a better understanding of the behaviour of the solutions. The employed strategies are dependable, uncomplicated, and effective; yet have not been utilised with the governing model in the literature that is now accessible. The resulting outcomes have impressive applications across a large number of study areas and computational physics phenomena representing real-world scenarios. The 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： chiral solitons exact solutions solitons stability analysis the nonlinear Schrödinger 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

New solitary wave and other exact solutions of the van der Waals normal form for granular materials

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Journal of Ocean Engineering and Science 2022年第2期7卷 170-177页

作者： Asim Zafar Tahir Mushtaq Aslam Malik ahmet bekir Department of Mathematics COMSATS University IslamabadVehari CampusPakistan Department of Mathematics University of the PunjabLahorePakistan Neighbourhood of Akcaglan Imarli StreetNumber:28/426030EskisehirTurkey

The investigation of exact solitary wave solutions to the nonlinear partial differential equation plays an important role to understand any physical phenomena in diverse applied *** current work is re-lated to the most prominent nonlinear model named as the van der Waals normal form that appeared naturally and also industrially for the granular *** oceanography,the sea ice,sand and snow are some examples of aforesaid matter among *** employ two novel integration approaches named as the simplest equation method and the exp a function method to explore the above mentioned van der Waals *** a backlash,many new solitary waves and other exact solutions are *** ob-tained results depict that the used approaches are simple and effective to deal with nonlinear ***,the numerical simulation of some solutions via two and three dimension graphical configurations are presented for certainty and exactness.

关键词： Van der Waals equation Novel integration schemes Solitary wave 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

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： Fisher型方程变系数非线性方程时变系数周期解奇异解假设方法单孤子解解的存在性

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 Duffing model and nonlinear fractional diffusion–reaction equation. The fractional derivatives are described in the modified Riemann–Liouville sense. The fractional complex transform 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：分数微分方程精确解数学生物学非线性反应扩散方程分数阶微分方程 Liouville 分数阶导数符号计算