Type: Article
Publication Date: 2010-02-18
Citations: 19
DOI: https://doi.org/10.1088/1751-8113/43/10/105204
The generalized sine-Gordon (sG) equation was derived as an integrable generalization of the sG equation. In this paper, we develop a direct method for solving the generalized sG equation without recourse to the inverse scattering method. In particular, we construct multisoliton solutions in the form of parametric representation. We obtain a variety of solutions which include kinks, loop solitons and breathers. The properties of these solutions are investigated in detail. We find a novel type of solitons with a peculiar structure that the smaller soliton travels faster than the larger soliton. We also show that the short-pulse equation describing the propagation of ultra-short pulses is reduced from the generalized sG equation in an appropriate scaling limit. Subsequently, the reduction to the sG equation is briefly discussed.