A defocusing complex short pulse equation and its multi-dark soliton solution by Darboux transformation

TL;DR

This paper introduces a new defocusing complex short pulse equation modeling ultra-short pulse propagation in optical fibers and constructs multi-dark soliton solutions using Darboux transformation, analyzing their properties.

Contribution

It proposes a novel defocusing complex short pulse equation and derives explicit multi-dark soliton solutions via Darboux transformation, expanding the understanding of ultra-short pulse dynamics.

Findings

Explicit one- and two-dark soliton solutions are obtained.

The properties and dynamics of the solitons are analyzed and illustrated.

The equation serves as an analogue to the nonlinear Schrödinger equation in the ultra-short regime.

Abstract

In this paper, we propose a complex short pulse equation of both focusing and defocusing types, which governs the propagation of ultra-short pulses in nonlinear optical fibers. It can be viewed as an analogue of the nonlinear Schr\"odinger (NLS) equation in the ultra-short pulse regime. Furthermore, we construct the multi-dark soliton solution for the defocusing complex short pulse equation through the Darboux transformation and reciprocal (hodograph) transformation. One- and two-dark soliton solutions are given explicitly, whose properties and dynamics are analyzed and illustrated.