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Dynamics in Nonlinear Schrödinger Equation with dc bias: From Subdiffusion to Painlevé Transcendent

Published online by Cambridge University Press:  24 April 2013

A. Iomin
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Abstract

Dynamics of the nonlinear Schrödinger equation in the presence of a constant electric field is studied. Both discrete and continuous limits of the model are considered. For the discrete limit, a probabilistic description of subdiffusion is suggested and a subdiffusive spreading of a wave packet is explained in the framework of a continuous time random walk. In the continuous limit, the biased nonlinear Schrödinger equation is shown to be integrable, and solutions in the form of the Painlevé transcendents are obtained.

Keywords

continuous time random walksubdiffusionfractional Fokker-Planck equationStark ladderself-accelerating solution
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 2: Anomalous diffusion , 2013 , pp. 88 - 99
Copyright
© EDP Sciences, 2013

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