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2013 Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations
Xiaoxiao Zheng, Yadong Shang, Yong Huang
Abstr. Appl. Anal. 2013(SI24): 1-7 (2013). DOI: 10.1155/2013/109690


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.


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Xiaoxiao Zheng. Yadong Shang. Yong Huang. "Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations." Abstr. Appl. Anal. 2013 (SI24) 1 - 7, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1300.35128
MathSciNet: MR3147792
Digital Object Identifier: 10.1155/2013/109690

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI24 • 2013
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