Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation |
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| Authors: | Chen Yong Li Biao and Zhang Hong-Qing |
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| Affiliation: | Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; State Key Laboratory of Mathematics & Mechanization, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | Based on the computerized symbolic system Maple and a Riccati equation, a Riccati equation expansion method is presented by a general ansatz. Compared with most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nonlinear differential equations. Making use of the method, we study the Bogoyavlenskii's generalized breaking soliton equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions. |
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| Keywords: | generalized Riccati equation expansion Bogoyavlenskii's generalized breaking soliton equation soliton-like solution periodic form solution |
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