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

Qing Tian, Lei Wu, Jie Fang Zhang, Boris A. Malomed, D. Mihalache, W. M. Liu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number016602
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume83
Issue number1
DOIs
StatePublished - 18 Jan 2011

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