Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC

R. A. Kraenkel, Nakkeeran Kaliyaperumal, K. W. Chow

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Abstract

We investigate the nonlinear Schrödinger equation with a time-dependent nonlinear coefficient. By means of Painlevé analysis we establish the integrability for a particular form of the nonlinear coefficient. The corresponding soliton solution is shown to be of the self-similar kind. We discuss the implications of the result to the dynamics of attractive Bose-Einstein condensates under Feshbach-managed nonlinearity and explore the possibility of a managed self-similar evolution in 1D condensates.

Original languageEnglish
Pages (from-to)86-92
Number of pages7
JournalCommunications in Nonlinear Science & Numerical Simulation
Volume16
Issue number1
Early online date15 Mar 2010
DOIs
Publication statusPublished - Jan 2011

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NLS Equation
Integrable Equation
Solitons
Nonlinear equations
Bose-Einstein Condensate
Condensate
Coefficient
Soliton Solution
Integrability
Nonlinear Equations
Nonlinearity
Form

Keywords

  • nonlinear Schrodinger equation
  • Bose–Einstein condensate (BEC)
  • Soliton
  • Hirota bilinear method

Cite this

Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC. / Kraenkel, R. A.; Kaliyaperumal, Nakkeeran; Chow, K. W.

In: Communications in Nonlinear Science & Numerical Simulation, Vol. 16, No. 1, 01.2011, p. 86-92.

Research output: Contribution to journalArticle

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