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

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

doi:10.1016/j.cnsns.2010.03.006

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

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

Engineering

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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 language	English
Pages (from-to)	86-92
Number of pages	7
Journal	Communications in Nonlinear Science & Numerical Simulation
Volume	16
Issue number	1
Early online date	15 Mar 2010
DOIs	https://doi.org/10.1016/j.cnsns.2010.03.006
Publication status	Published - Jan 2011

Keywords

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

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10.1016/j.cnsns.2010.03.006

Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC
NOTICE: this is the author’s version of a work that was accepted for publication in Communications in Nonlinear Science & Numerical Simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION, [VOL 16, ISSUE 1, (2011)] DOI 10.1016/j.cnsns.2010.03.006
Accepted author manuscript, 134 KB

Cite this

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abstract = "We investigate the nonlinear Schr{\"o}dinger equation with a time-dependent nonlinear coefficient. By means of Painlev{\'e} 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.",

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AB - 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.

KW - nonlinear Schrodinger equation

KW - Bose–Einstein condensate (BEC)

KW - Soliton

KW - Hirota bilinear method

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JF - Communications in Nonlinear Science & Numerical Simulation

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

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