Exact wave solutions for the nonlinear time fractional Sharma-Tasso-Olver equation and the fractional Klein-Gordon equation in mathematical physics

Ripan Roy; M. Ali Akbar; Abdul Majid Wazwaz

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Exact wave solutions for the nonlinear time fractional Sharma-Tasso-Olver equation and the fractional Klein-Gordon equation in mathematical physics

机译：数学物理学中非线性时间分数分数Sharma-Tasso-Olver方程和分数Klein-Gordon方程的精确波解

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摘要

In this study, we examine the resourceful traveling wave solutions of a pair of nonlinear time fractional differential equations, namely, the general time fractional Sharma-Tasso-Olver equation and the fractional Klein-Gordon equation in the form of hyperbolic functions, trigonometric functions, and rational functions along with free parameters. To establish above mentioned type of solutions those are factual, convenient to use and penetrate the fission and fusion phenomena take place in solitons, the relativistic energy-momentum relation, scalar electrodynamics, electromagnetic interactions, plasma physics, nuclear physics etc. very clearly, we implement the new generalized (G'/G)-expansion method. We emphasize that this method is highly effective and a forcible mathematical tool to extract solitary wave solutions of the time fractional models that are extensively used in theoretical physics.

机译：在这项研究中，我们以双曲函数，三角函数形式，研究了一对非线性时间分数阶微分方程（即通用时间分数Sharma-Tasso-Olver方程和分数Klein-Gordon方程）的足智多用的行波解，合理的功能以及自由参数。要建立上述类型的解决方案，这些解决方案应是事实，方便使用并渗透裂变和聚变现象，发生在孤子，相对论能量动量关系，标量电动力学，电磁相互作用，等离子体物理学，核物理学等中。实施新的广义（G'/ G）扩展方法。我们强调，该方法是一种有效的方法，并且是一种用于提取时间分数模型的孤波解的强制性数学工具，这些时间分数模型在理论物理学中得到了广泛使用。

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来源
《Optical and quantum electronics》 |2018年第1期|25.1-25.19|共19页
作者
Ripan Roy; M. Ali Akbar; Abdul Majid Wazwaz;
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作者单位

Department of Applied Mathematics, Gono Bishwabidyalay, Dhaka, Bangladesh;

Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh;

Department of Mathematics, Saint Xavier University, Chicago, IL, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
The general time fractional Sharma-Tasso-Olver equation; The nonlinear fractional Klein-Gordon equation; Generalized (G'/G)-expansion method; Traveling wave solutions; Soliton;

机译：通用时间分数Sharma-Tasso-Olver方程;非线性分数Klein-Gordon方程;广义（G'/ G）展开方法;行波解决方案;孤子;

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2. The first integral method and its application for finding the exact solutions of nonlinear fractional partial differential equations (PDES) in the mathematical physics [J] . Elsayed M. E. Zayed, Yasser A. Amer International Journal of Physical Sciences . 2014,第8期

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3. Explicit solutions for space-time fractional partial differential equations in mathematical physics by a new generalized fractional Jacobi elliptic equation-based sub-equation method [J] . Feng Qinghua, Meng Fanwei Optik: Zeitschrift fur Licht- und Elektronenoptik: = Journal for Light-and Electronoptic . 2016,第19期

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4. The Investigation of Exact Solutions of Nonlinear Time-Fractional Klein-Gordon Equation by Using Generalized Kudryashov Method [C] . Seyma Tuluce Demiray, Yusuf Pandir, Hasan Bulut International Conference on Mathematical Problems in Engineering and Aerospace Sciences . 2014

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5. Time-Domain Analysis of Fractional Wave Equations and Implementations of Perfectly Matched Layers in Nonlinear Ultrasound Simulations. [D] . Zhao, Xiaofeng. 2018

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6. Solitary wave solutions to some nonlinear fractional evolution equations in mathematical physics [O] . H.M. Shahadat Ali, M.A. Habib, M.Mamun Miah, 2020

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Exact wave solutions for the nonlinear time fractional Sharma-Tasso-Olver equation and the fractional Klein-Gordon equation in mathematical physics

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