Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013Anomalous diffusion
|Page(s)||88 - 99|
|Published online||24 April 2013|
Dynamics in Nonlinear Schrödinger Equation with dc bias: From Subdiffusion to Painlevé Transcendent
Department of Physics and Solid State Institute, Technion - Israel Institute
of Technology, Haifa, 32000, Israel
⋆ Corresponding author. E-mail: email@example.com
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.
Mathematics Subject Classification: 60J25 / 60H30 / 60J60
Key words: continuous time random walk / subdiffusion / fractional Fokker-Planck equation / Stark ladder / self-accelerating solution
© EDP Sciences, 2013
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