New exact traveling wave solutions for double Sine–Gordon equation

摘要

Under the assumption that u′ is a function form of einu, this paper presents a new set of traveling-wave solutions with JacobiAmplitude function for the generalized form of the double Sine–Gordon equation utt=kuxx+2αsin(nu)+βsin(2nu). The presented solutions are compared to previous ones which are derived from Tanh method and other variable separated method. We find that some special case of the proposed solutions (fixing the integral constant to a particular value) involve in some previous results presented in Wazwaz (2006).