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

Qing Tian, Lei Wu, J. F. Zhang, B. A. Malomed, D. Mihalache, W. M. Liu

Research output: Contribution to journalArticle

24 Citations (Scopus)

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.
LanguageEnglish
Article number016602
Number of pages5
JournalPhysical Review E
Volume83
Issue number1
DOIs
Publication statusPublished - Jan 2011

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control stability
Nonlinear Schrodinger Equation
Soliton Solution
nonlinear equations
Solitons
solitary waves
nonlinearity
Nonlinearity
Harmonic Potential
Energy Levels
Harmonic Oscillator
Nonlinear Schrödinger Equation
defocusing
Modulation
harmonic oscillators
Exact Solution
Higher Order
Eigenvalue
eigenvalues
energy levels

Keywords

  • modes
  • soliton solutions
  • nonlinear Schrödinger equation

Cite this

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abstract = "We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schr{\"o}dinger 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.",
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Exact soliton solutions and their stability control in the nonlinear Schrodinger equation with spatiotemporally modulated nonlinearity. / Tian, Qing; Wu, Lei; Zhang, J. F.; Malomed, B. A.; Mihalache, D.; Liu, W. M.

In: Physical Review E, Vol. 83, No. 1, 016602, 01.2011.

Research output: Contribution to journalArticle

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