Scattering properties of envelope solitons in disordered systems: decay of localization effects by strong nonlinearity

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Show simple item record Kivshart, Yuri S. Gredeskul, Sergei A. Sánchez, Angel Vázquez, Luis 2012-08-01T09:21:07Z 2012-08-01T09:21:07Z 1992
dc.identifier.bibliographicCitation Waves in Random Media, vol. 2, n. 2, 1992. Pp. 125-140
dc.identifier.issn 0959-7174 (print version)
dc.identifier.issn 1745-5049 (online version)
dc.description.abstract We study the scattering of nonlinear wavepackets in the form of envelope soli tons by a one-dimensional disordered system. We briefly review the features of the scattering for linear waves and obtain some results for linear wave packets to demonstrate their common exponential decay of the transmission coefficient, characterized by a localization length. We consider the same process for envelope solitons, and we show in the framework of the simplest model, that, above a certain threshold, strong non linearity allows undistorted propagation of these wavepackets. We describe how this behaviour can be obtained, for the nonlinear Schriidinger equation, by means of a simple independent scattering approach, using results of soliton perturbation theory to compute one-impurity reflection coefficients in the Born approximation. We derive equations to describe the transmission of the soli ton parameters and we analyse them in full detail. The main result of our study is the conclusion that a strong nonlinearity stipulates two spatial scales in the wavepacket scattering by disordered systems. The first spatial scale depends on the amplitude and it may be very large, and the second one is the usual localization length. As a consequence the non linear wavepackets or solitons are much more stable against disorder than linear ones.
dc.description.sponsorship All the numerical work was carried out using the IBM 3090 computer at the Centro de Investigaciones Energeticas, Medio Ambientales y Tecnol6gicas (CIEMAT), Spain, which we gratefully acknowledge. Two of us (A S and L V) are grateful for financial support from the Universidad Complutense de Madrid and the Direcci6n General de Investigación Cientifica y Tecnica, under grant PB86-000S.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Taylor & Francis
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.title Scattering properties of envelope solitons in disordered systems: decay of localization effects by strong nonlinearity
dc.type article
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1088/0959-7174/2/2/004
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
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