A direct method for solving the generalized sine-Gordon equation

Details A direct method for solving the generalized sine-Gordon equation A direct method for solving the generalized sine-Gordon equation

2010-01-28

arxiv.org/abs/1001.5128v1

Nonlinear Sciences

Pattern Formation and Solitons

To appear in J. Phys. A: Math. Theore. 43(2010)

Scientific paper

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.

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