Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations
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 functi...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/109690 |
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| 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. |
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| ISSN: | 1085-3375 1687-0409 |