Abstract In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota--Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.
Received: 03 January 2002
Revised: 20 September 2002
Published: 20 January 2003
(Partial differential equations)
Fund: Project supported by the National Natural Science Foundation of China (Grant No 1007201), the State Key Development Programme for Basic Research of China (Grant No G1998030600), and the Doctorate Fund of the State Education Commission of China (Grant No 98014119).
Cite this article:
Cheng Yong, Yan Zhen-Ya, Li Biao, Zhang Hong-Qing New explicit exact solutions for a generalized Hirota-Satsuma coupled KdV system and a coupled MKdV equation 2003 Chin. Phys. 12 1