On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method

Document Type : Research Paper

Authors

1 Peoples' Friendship University of Russia (RUDN University), Moscow, Russia.

2 Gubkin Russian State University of Oil and Gas, Moscow, Russia.

3 Kazan Federal University, Kazan, Russia.

4 Don State Technical University, Rostov-on-Don, Russia.

5 Kuban State University, Krasnodar, Russia.

Abstract

The generalized ( G′/G )-expansion method with the aid of Maple is proposed to seek exact solutions of nonlinear evolution equations. For finding exact solutions are expressed three types of solutions that include hyperbolic function solution, trigonometric function solution, and rational solution. The article studies the Zakharov–Kuznetsov (ZK) equation, the generalized ZK (gZK) equation, and the generalized forms of these equations. Exact solutions with traveling wave solutions of nonlinear evolution equations are obtained. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations.

Keywords

Main Subjects

Computational Methods for Differential Equations
Volume 13, Issue 1
January 2025
Pages 258-270

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History

  • Receive Date: 24 April 2024
  • Revise Date: 08 May 2024
  • Accept Date: 08 May 2024

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