Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation
Chen Yong (陈勇), Li Biao (李彪), Zhang Hong-Qing (张鸿庆)
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; State Key Laboratory of Mathematics & Mechanization, Chinese Academy of Sciences, Beijing 100080, China
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.
Received: 08 January 2003
Revised: 31 March 2003
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10072013), and the State Key Development Programme for Basic Research of China (Grant No G1998030600).
Cite this article:
Chen Yong (陈勇), Li Biao (李彪), Zhang Hong-Qing (张鸿庆) Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation 2003 Chinese Physics 12 940
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
