The reduced transformation equations and group invariant solutions of Dodd-Bullough-Mikhailov(DBM)were given by using Lie group analysing method.The travelling wave solutions of the DBM equation and exact solutions of the reduced transformation equation of the DBM equation were found by using the method of extended tanh-function,respectively.The φ(ξ)-expansion method was proposed by using the reduced transformation equation of the DBM equation and its explicit exact solutions.The hyperbolic,trigonometric,rational function and periodic type explicit travelling solutions of seventh order KdV equation,fifth order Kawahara and Caudrey-Dodd-Gibbon equation were presented by φ(ξ)-expansion method.The dynamic behavior of some travelling wave solutions were also analyzed.Moreover,the φ(ξ)-expansion method can be used to solve some other nonlinear evolution equations.
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