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Zbl 1088.65087
Chen, Yong; Wang, Qi
A new elliptic equation rational expansion method and its application to the shallow long wave approximate equations. (English)
[J] Appl. Math. Comput. 173, No. 2, 1163-1182 (2006). ISSN 0096-3003

Summary: A new elliptic equation rational expansion method is presented by a new general ansatz, which is a direct and unified algebraic method for constructing multiple and more general travelling wave solution for nonlinear partial differential equation and implemented in a computer algebraic system. The proposed method is applied to consider the shallow long wave approximate equation and obtains rich new families of the exact solutions, including rational form solitary wave, rational form triangular periodic, rational form Jacobi and Weierstrass doubly periodic solutions.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35Q51 Solitons
68W30 Symbolic computation and algebraic computation

Keywords: travelling wave solution; elliptic equation rational expansion method; rational form solitary wave solutions; shallow long wave approximate equation; rational form triangular periodic solutions; rational form Jacobi doubly periodic solutions; symbolic computation; solitons; Weierstrass doubly periodic solutions

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