Dynamics in Nonlinear Schrodinger Equation with dc bias: From Subdiffusion to Painleve Transcendent

作者：Iomin A^*

来源：Mathematical Modelling of Natural Phenomena, 2013, 8(2): 88-99.

DOI：10.1051/mmnp/20138206

• continuous time random walk
• subdiffusion
• fractional Fokker-Planck equation
• Stark ladder
• self-accelerating solution

Dynamics of the nonlinear Schrodinger 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 Schrodinger equation is shown to be integrable, and solutions in the form of the Painleve transcendents are obtained.

• 出版日期2013