Symbolic computation and construction of soliton-like solutions for a breaking soliton equation |
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Authors: | Biao Li Yong Chen Hengnong Xuan Hongqing Zhang |
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Institution: | a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, People’s Republic of China b Department of Computer, Nanjing University of Economics, Nanjing 210003, People’s Republic of China |
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Abstract: | Based on the symbolic computation system––Maple and a Riccati equation, by introducing a new more general ansätz than the ansätz in the tanh method, extended tanh-function method, modified extended tanh-function method, generalized tanh method and generalized hyperbolic-function method, we propose a generalized Riccati equation expansion method for searching for exact soliton-like solutions of nonlinear evolution equations and implemented in computer symbolic system––Maple. Making use of our method, we study a typical breaking soliton equation and obtain new families of exact solutions, which include the nontravelling wave’ and coefficient function’ soliton-like solutions, singular soliton-like solutions and periodic solutions. The arbitrary functions of some solutions are taken to be some special constants or functions, the known solutions of this equation can be recovered. |
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