Lie Symmetries, Conservation Laws and Solutions for (4+1)-Dimensional Time Fractional KP Equation with Variable Coefficients in Fluid Mechanics
Year: 2024
Author: Xiuqi He, Changna Lu, Cunjuan Hou
Journal of Information and Computing Science, Vol. 19 (2024), Iss. 2 : pp. 103–130
Abstract
In recent years, high-dimensional fractional equations have gained prominence as a pivotal focus of interdisciplinary research spanning mathematical physics, fluid mechanics, and related fields. In this paper, we investigate a (4+1)-dimensional time-fractional Kadomtsev-Petviashvili (KP) equation with variable coefficients. We first derive the (4+1)-dimensional time-fractional KP equation with variable coefficients in the sense of the Riemann-Liouville fractional derivative using the semi-inverse and variational methods. The symmetries and conservation laws of this equation are analyzed through Lie symmetry analysis and a new conservation theorem, respectively. Finally, both exact and numerical solutions of the fractional-order equation are obtained using the Hirota bilinear method and the pseudo-spectral method. The effectiveness and reliability of the proposed approach are demonstrated by comparing the numerical solutions of the derived models with exact solutions in cases where such solutions are known.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/JICS-2024-007
Journal of Information and Computing Science, Vol. 19 (2024), Iss. 2 : pp. 103–130
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Time fractional equation Conservation laws Hirota bilinear method Pseudo-spectral method.