Classical Lie symmetry group analysis and exact solutions of the fractional modified (2+1)-dimensional Zakharov-Kuznetsov equation

Subject Areas : هندسه

Mir Sajjad Hashemi ¹ , Ali Haji Badali ² , Farzaneh Alizadeh ³

1 - Associate professor/Department of Mathematics, University of Bonab, Bonab, Iran,
2 - Professor/Department of Mathematics, University of Bonab, Bonab, Iran,
3 - PhD. student/Department of Mathematics, University of Bonab, Bonab, Iran,

Received: 2021-05-30 Accepted : 2023-01-31 Published : 2022-06-22

Keywords: تقارنی‌های لی, زاخاروف کوزنتسو بهبود یافته, تقارنی‌های کلاسیک, معادلات دیفرانسیل کسری با مشتقات جزئی,

Abstract :

In this paper, we consider the classical Lie symmetries of fractional modified Zakharov Kuznetsov (which in this paper we abbreviately show this by the mZK equation) equation. Indeed, Lie symmetries are utilized for solving the nonlinear fractional three-dimensional mZK equation with partial derivatives, and by using the infinitesimal transformations and corresponding invariant solutions, we reduce the underlying equation one dimension less than the original mZK equation, and finally, some of the corresponding exact solutions are extracted.Indeed, Lie groups are geometric powerful tools for analyzing and investigating a wide variety of classes of equations such as ordinary differential equations, partial differential equations, fractional differential equations, and integral and integro differential equations. Invariant solutions and conservation laws that play a very significant and astonishing role in physical science can be obtained by this method. Moreover, various kinds of this method such as classical, non-classical, approximate and et cetera can be extracted by utilized in this field.

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