Multicomponent integrable wave equations II: Soliton solutions

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.

24 pages, 10 figures, standard LaTeX2e, submitted for publication

References in corpus (5)

• Multicomponent integrable wave equations I. Darboux-Dressing Transformation
• Stable Control of Pulse Speed in Parametric Three-Wave Solitons
• Exact solutions of the 3-wave resonant interaction equation
• Inelastic Scattering and Interactions of Three-Wave Parametric Solitons
• Parametric Frequency Conversion of Short Optical Pulses Controlled by a CW Background

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• Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide
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• Exact solutions of multicomponent nonlinear Schrödinger equations under general plane-wave boundary conditions
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• Discretizations of the generalized AKNS scheme
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