The time-fractional mZK equation for gravity solitary waves and solutions using sech-tanh and radial basic function method
Articles
Min Guo
Shandong University of Science and Technology
Haoyu Dong
Shandong University of Science and Technology
Jianxin Liu
Qufu Normal University
Hongwei Yang
Shandong University of Science and Technology
Published 2018-12-14
https://doi.org/10.15388/NA.2019.1.1
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Keywords

gravity solitary waves
time-fractional mZK equation
sech-tanh method
radial basis function method

How to Cite

Guo, M. (2018) “The time-fractional mZK equation for gravity solitary waves and solutions using sech-tanh and radial basic function method”, Nonlinear Analysis: Modelling and Control, 24(1), pp. 1–19. doi:10.15388/NA.2019.1.1.

Abstract

In recent years, we know that gravity solitary waves have gradually become the research spots and aroused extensive attention; on the other hand, the fractional calculus have been applied to the biology, optics and other fields, and it also has attracted more and more attention. In the paper, by employing multi-scale analysis and perturbation methods, we derive a new modified Zakharov–Kuznetsov (mZK) equation to describe the propagation features of gravity solitary waves. Furthermore, based on semi-inverse and Agrawal methods, the integer-order mZK equation is converted into the time-fractional mZK equation. In the past, fractional calculus was rarely used in ocean and atmosphere studies. Now, the study on nonlinear fluctuations of the gravity solitary waves is a hot area of research by using fractional calculus. It has potential value for deep understanding of the real ocean–atmosphere. Furthermore, by virtue of the sech-tanh method, the analytical solution of the time-fractional mZK equation is obtained. Next, using the above analytical solution, a numerical solution of the time-fractional mZK equation is given by using radial basis function method. Finally, the effect of time-fractional order on the wave propagation is explained.

 

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