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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.
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Chen et al. (2003) studied this question.
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