Abundant explicit and exact solutions for the variable coefficient mKdV equations
type: Item
instance of: scholarly article
title: Abundant explicit and exact solutions for the variable coefficient mKdV equations
zbMATH Open document ID: 1300.35128
DOI: 10.1155/2013/109690
author: Xiaoxiao Zheng
author: Yadong Shang
author: Yong Huang
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 33E05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 6306030
zbMATH Keywords: exact solutions
zbMATH Keywords: variable coefficients mKdV (VC-mKdV) equation
zbMATH Keywords: Mathematica
Wikidata QID: Q58915298
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/109690
OpenAlex ID: W2133476030
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description: scientific article; zbMATH DE number 6306030