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An Instability Criterion for Nonlinear Standing Waves on Nonzero Backgrounds

Jackson, RK and Marangell, R and Susanto, H (2014) 'An Instability Criterion for Nonlinear Standing Waves on Nonzero Backgrounds.' Journal of Nonlinear Science, 24 (6). 1177 - 1196. ISSN 0938-8974

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Abstract

© 2014, Springer Science+Business Media New York. A nonlinear Schrödinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a finite interval. Localized standing wave solutions on a non-zero background, e.g., dark solitons trapped by the inhomogeneity, are identified and studied. A novel instability criterion for such states is established through a topological argument. This allows instability to be determined quickly in many cases by considering simple geometric properties of the standing waves as viewed in the composite phase plane. Numerical calculations accompany the analytical results.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 12 Nov 2014 19:47
Last Modified: 30 Jan 2019 16:19
URI: http://repository.essex.ac.uk/id/eprint/11555

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