Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 221, Issue 1, Pages 31-36Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2006.07.002
Keywords
nonlinear Schrodinger equations; similarity transformations
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In this paper we obtain a similarity transformation connecting nonlinear Schrodinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrodinger equation. As applications we construct exact breathing solutions to multidimensional non-autonomous nonlinear Schrodinger equations and discuss how to construct time-dependent coefficients leading to solutions which collapse weakly in three-dimensional scenarios. Our results are applicable to the study of the dynamics of Bose-Einstein condensates in the mean-field limit and dispersion-managed optical systems. (c) 2006 Elsevier B.V. All rights reserved.
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