Taming spatiotemporal chaos by impurities in the parametrically driven damped nonlinear Schrödinger equation

N. V. Alexeeva; I. V. Barashenkov; G. P. Tsironis

doi:10.2991/jnmp.2001.8.s.2

Taming spatiotemporal chaos by impurities in the parametrically driven damped nonlinear Schrödinger equation

N. V. Alexeeva, I. V. Barashenkov, G. P. Tsironis

Department of Physics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Solitons of the parametrically driven, damped nonlinear Schrödinger equation become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the chaos can be suppressed by introducing localized inhomogeneities in the parameters of the equation. The pinning of the soliton on an "attractive"inhomogeneity expands its stability region whereas "repulsive"impurities produce an effective partitioning of the interval. We also show that attractive impurities may spontaneously nucleate solitons which subsequently remain pinned on these defects. A brief account of these results has appeared in patt-sol/9906001, where the interested reader can also find multicolor versions of the figures.

Original language	English
Pages (from-to)	5-12
Number of pages	8
Journal	Journal of Nonlinear Mathematical Physics
Volume	8
Issue number	SUPPL.
DOIs	https://doi.org/10.2991/jnmp.2001.8.s.2
Publication status	Published - Feb 1 2001

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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AB - Solitons of the parametrically driven, damped nonlinear Schrödinger equation become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the chaos can be suppressed by introducing localized inhomogeneities in the parameters of the equation. The pinning of the soliton on an "attractive"inhomogeneity expands its stability region whereas "repulsive"impurities produce an effective partitioning of the interval. We also show that attractive impurities may spontaneously nucleate solitons which subsequently remain pinned on these defects. A brief account of these results has appeared in patt-sol/9906001, where the interested reader can also find multicolor versions of the figures.

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