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Abundant wave solutions of conformable space-time fractional order Fokas wave model arising in physical sciences
Alexandria Engineering Journal ( IF 6.8 ) Pub Date : 2021-01-21 , DOI: 10.1016/j.aej.2021.01.001
Shahzad Sarwar , Khaled M. Furati , Muhammad Arshad

The higher dimensional Fokas equation is the integrable expansion of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations. The Fokas model has an important role in wave theory, to describe the physical phenomena of waves on the surface and inside the water. This article deals with the (4+1)-dimensional conformable space-time fractional-order Fokas partial differential equation. Two efficient methods, namely the generalized exp(-ϕ(ξ))-expansion and improved F-expansion methods, are formulated for conformable fractional-order partial differential equation and new wave structures of fractional order Fokas model are constructed. The different kinds of new solitons are achieved such as bright soliton, dark soliton, Kink and anti-kink solitons, periodic solitary waves, and traveling waves. These new soliton waves are constructed at some values of fractional order α and using different parametric values of the methods by using the software package Mathematica. Newly obtained soliton solutions are compared with the available soliton solutions with different fractional derivatives in the literature. Some of the achieved results are explained 2D and 3D graphically. The new results interpreting that these obtained solutions can be a part, to complete the family of solutions and considered methods are effective, simple, and easy to use. Furthermore, this paper gives an idea, how can reduce the conformable fractional order higher dimensional partial differential equation into an ODE of one variable to obtain the exact solutions. These results and methods can be help to investigate the other higher-dimensional conformable fractional-order models which appear in nonlinear wave theory such as optics, quantum gases, hydrodynamics, photonics, plasmas, and solid-state physics.



中文翻译:

物理科学中产生的适时空分数阶Fokas波模型的丰富波解

高维Fokas方程是Kadomtsev-Petviashvili(KP)和Davey-Stewartson(DS)方程的可积展开。Fokas模型在波浪理论中起着重要作用,用于描述波浪在水面和内部的物理现象。本文涉及4+1个维适时空分数阶Fokas偏微分方程。两种有效的方法,即广义exp--ϕξ拟定了适用于分数阶偏微分方程的展开式和改进的F展开法,并构造了分数阶Fokas模型的新波结构。实现了各种新的孤子,例如亮孤子,暗孤子,扭结和反扭孤子,周期性孤波和行波。这些新的孤波以分数阶的一些值构造α并使用软件包Mathematica使用不同方法的参数值。在文献中将新获得的孤子溶液与具有不同分数导数的可用孤子溶液进行了比较。某些获得的结果将以图形方式在2D和3D中进行解释。新结果表明,这些获得的解决方案可以成为解决方案系列的一部分,并且认为这些方法有效,简单且易于使用。此外,本文给出了一个想法,如何将服从分数阶高维偏微分方程简化为一个变量的ODE以获得精确解。这些结果和方法有助于研究非线性波理论中出现的其他高维适形分数阶模型,例如光学,量子气体,

更新日期:2021-01-22
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