Multiloop Soliton and Multibreather Solutions of the Short Pulse Model Equation

Abstract

We develop a systematic procedure for constructing the multisoliton solutions of the short pulse (SP) model equation which describes the propagation of ultra-short pulses in nonlinear media. We first introduce a novel hodograph transformation to convert the SP equation into the sine-Gordon (sG) equation. With the soliton solutions of the sG equation, the system of linear partial differential equations governing the inverse mapping can be integrated analytically to obtain the soliton solutions of the SP equation in the form of the parametric representation. By specifying the soliton parameters, we obtain the multiloop and multibreather solutions. We investigate the asymptotic behavior of both solutions and confirm their solitonic feature. The nonsingular breather solutions may play an important role in studying the propagation of ultra-short pulses in an optical fibre.