Asymptotic localization of stationary states in the nonlinear Schrödinger equation

Abstract : The mapping of the Nonlinear Schrödinger Equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth rates of the moments of the wave function and its derivative for the linear Schrödinger Equation in a random potential are computed analytically and resummation is used to obtain the corresponding growth rate for the nonlinear Schrödinger equation and the localization length of the stationary states.