Geodesic
Dynamics in Nonlinear Schrödinger Equation with dc bias: From Subdiffusion to Painlevé Transcendent
A. Iomin1
1 Department of Physics and Solid State Institute, Technion - Israel Institute of Technology, Haifa, 32000, Israel
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 2, pp. 88-99

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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.
DOI : 10.1051/mmnp/20138206

A. Iomin 1

1 Department of Physics and Solid State Institute, Technion - Israel Institute of Technology, Haifa, 32000, Israel 
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A. Iomin. Dynamics in Nonlinear Schrödinger Equation with dc bias: From Subdiffusion to Painlevé Transcendent. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 2, pp. 88-99. doi: 10.1051/mmnp/20138206

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