Multicomponent integrable wave equations II: Soliton solutions

TL;DR

This paper applies Darboux Dressing Transformations to construct soliton solutions for multicomponent boomeronic wave equations, including a novel three-pulse simulton solution in a resonant three-wave interaction model.

Contribution

It extends previous work by deriving explicit soliton solutions, including a new simulton, for a class of multicomponent boomeronic equations using Darboux transformations.

Findings

Constructed one-soliton solutions from vacuum and plane wave states

Specialized solutions for resonant three-wave interaction model

Introduced a novel three locked dark pulses simulton

Abstract

The Darboux Dressing Transformations developed in our previous paper (Multicomponent integrable wave equations I. Darboux-Dressing Transformation, J. Phys. A: Math. Theor. 40, 961-977, 2007) are here applied to construct soliton solutions for a class of boomeronic type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one soliton solutions. The formulae are specialised to the particularly interesting case of the resonant interaction of three waves, a well-known model which is of boomeronic type. For this equation a novel solution which describes three locked dark pulses (simulton) is introduced.