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The extended mapping method is proposed to obtain new exact solutions to a new Hamiltonian amplitude equation introduced by Wadati et al. [J. Phys. Soc. Jpn. 61 (1992) 1187]. The new periodic wave solutions are the linear combination of two Jacobi elliptic waves. Limit cases are studied, and new solitary wave solutions and triangular periodic wave solutions are got.
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Yan-ze Peng (2004) studied this question.
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