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Long-Time Behavior of the Schrodinger-Langevin Equation
by I-Liang Chern   Hai-Liang Li

Vol. 8 No. 4 (2013) P.505~P.544

ABSTRACT

We consider the large time behavior for nonlinear Schr\"odinger--Langevin equation in one dimension for WKB-initial data with different density at left/right far fields. We show that the momentum damping overwhelms the quantum dispersion. Thus, unlike those in scattering theory, the solution tends to an asymptotic state determined by a porous media equation. More precisely, the total density tends pointwise to a nonlinear diffusion wave and the phase tends to a corresponding function.

KEYWORDS
Nonlinear Scrödinger-Langevin equation, damping, long-time behavior, energy method, nonlinear diffusion waves

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35B40, 35Q53

MILESTONES