Explicit exact solutions for a new generalized Hamiltonian amplitude equation with nonlinear terms of any order

Author: Chen Yong  

Publisher: Springer Publishing Company

ISSN: 0044-2275

Source: Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol.55, Iss.6, 2004-11, pp. : 983-993

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Abstract

Making use of a proper transformation and a generalized ansatz, we consider a new generalized Hamiltonian amplitude equation with nonlinear terms of any order, iux + utt + (α|u|p + |u|2p)u + uxt = 0. As a result, many explicit exact solutions, which include kink-shaped soliton solutions, bell-shaped soliton solutions, periodic wave solutions, the combined formal solitary wave solutions and rational solutions, are obtained.