A direct method for solving the generalized sine-Gordon equation
Abstract
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 olutions 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.
Keywords
Cite
@article{arxiv.1001.5128,
title = {A direct method for solving the generalized sine-Gordon equation},
author = {Yoshimasa Matsuno},
journal= {arXiv preprint arXiv:1001.5128},
year = {2015}
}
Comments
To appear in J. Phys. A: Math. Theore. 43(2010)