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.

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

References in corpus (2)

• Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials
• Soliton and Periodic solutions of the Short Pulse Model Equation

Cited by in corpus (3)

• Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation
• Parametric solutions of the generalized short pulse equations
• A direct method for solving the generalized sine-Gordon equation II