Abstract and Applied Analysis

Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

Xiaoxiao Zheng, Yadong Shang, and Yong Huang

Full-text: Open access

Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 109690, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449829

Digital Object Identifier
doi:10.1155/2013/109690

Mathematical Reviews number (MathSciNet)
MR3147792

Zentralblatt MATH identifier
1300.35128

Citation

Zheng, Xiaoxiao; Shang, Yadong; Huang, Yong. Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 109690, 7 pages. doi:10.1155/2013/109690. https://projecteuclid.org/euclid.aaa/1393449829


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