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Exact Solutions of Gardner Equations through tanh-coth Method
Department of Mathematics, Zhejiang Normal University, Jinhua, China
Department of Mathematics, Zhejiang Normal University, Jinhua, China
Department of Mathematics, Zhejiang Normal University, Jinhua, China
Department of Mathematics, Zhejiang Normal University, Jinhua, China
- 1 Department of Mathematics, Zhejiang Normal University, Jinhua, China
- 2 Department of Mathematics, Zhejiang Normal University, Jinhua, China
- 3 Department of Mathematics, Zhejiang Normal University, Jinhua, China
- 4 Department of Mathematics, Zhejiang Normal University, Jinhua, China
Applied Mathematics·Volume 07 (2016)·Pages 2374–2381·Published 2 December 2016·DOI10.4236/am.2016.718186
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Abstract
In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable and effective in handling a large number of nonlinear dispersive and disperse equations. Through tanh-coth method, we get analytical expressions of soliton solutions of Gardner equations. The one-soliton solution is characterized by an infinite wing or infinite tail.
Keywordstanh-coth MethodGardner EquationsSoliton Solutions
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