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Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

Xiaoxiao Zheng
Yadong Shang
Yong Huang
Journal / Anthology

Abstract and Applied Analysis
Year: 2013

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 ofVC-mKdVequation, such as rational function solutions, periodicwave 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.