Soliton–radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation

We use the Riemann–Hilbert problem to study the interaction of the soliton with radiation in the parametrically driven, damped nonlinear Schrödinger equation. The analysis is reduced to the study of a four-dimensional dynamical system for the amplitude and phase of the soliton and the complex amplit...

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Bibliographic Details
Published inPhysica. D Vol. 164; no. 1; pp. 83 - 109
Main Authors Shchesnovich, V.S., Barashenkov, I.V.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2002
Subjects
Nonlinear
Parametric driving
Riemann–Hilbert problem
Schrödinger equation
Soliton-radiation coupling
Nonlinear
Parametric driving
Soliton-radiation coupling
Schrödinger equation
Riemann–Hilbert problem
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Summary:We use the Riemann–Hilbert problem to study the interaction of the soliton with radiation in the parametrically driven, damped nonlinear Schrödinger equation. The analysis is reduced to the study of a four-dimensional dynamical system for the amplitude and phase of the soliton and the complex amplitude of the long-wavelength radiation. In contrast to previously utilised inverse scattering-based perturbation techniques, our approach is valid for arbitrarily large driving strengths and damping coefficients. We show that, contrary to suggestions made in literature, the complexity observed in the soliton’s dynamics cannot be accounted for just by its coupling to the long-wavelength radiation.
ISSN:0167-2789
1872-8022
DOI:10.1016/S0167-2789(02)00358-5