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Exact soliton solutions and their stability control in the nonlinear Schrodinger equation with spatiotemporally modulated nonlinearity

Tian, Qing and Wu, Lei and Zhang, J. F. and Malomed, B. A. and Mihalache, D. and Liu, W. M. (2011) Exact soliton solutions and their stability control in the nonlinear Schrodinger equation with spatiotemporally modulated nonlinearity. Physical Review E, 83 (1). ISSN 1539-3755

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Abstract

We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schrödinger equation with a spatiotemporal modulation of the nonlinearity and external potentials. As an example, we construct exact solitons for the defocusing nonlinearity and harmonic potential. When the soliton’s eigenvalue is fixed, the number of exact solutions is determined by energy levels of the linear harmonic oscillator. In addition to the stable fundamental solitons, stable higher-order modes, describing array of dark solitons nested in a finite-width background, are constructed too. We also show how to control the instability domain of the nonstationary solitons.

Item type: Article
ID code: 40431
Keywords: modes, soliton solutions, nonlinear Schrödinger equation , Physics, Statistical and Nonlinear Physics, Statistics and Probability, Condensed Matter Physics
Subjects: Science > Physics
Department: Faculty of Engineering > Mechanical and Aerospace Engineering
Faculty of Engineering > Electronic and Electrical Engineering
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Depositing user: Pure Administrator
Date Deposited: 17 Jul 2012 14:36
Last modified: 05 Sep 2014 16:45
URI: http://strathprints.strath.ac.uk/id/eprint/40431

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