Chen Yong et al 2003 Chinese Phys. 12 940 doi:10.1088/1009-1963/12/9/303
Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation
Chen Yong, Li Biao and Zhang Hong-Qing
Show affiliationsBased 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.
- PACS
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02.30.Hq Ordinary differential equations
- Subjects
- Dates
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Issue 9 ( 1 September 2003)
Received 8 January 2003, in final form 31 March 2003
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Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation
Chen Yong et al 2003 Chinese Phys. 12 940
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