Averaging Principle for the Higher Order Nonlinear Schrodinger Equation with a Random Fast Oscillation

作者：Gao, Peng^*

来源：Journal of Statistical Physics, 2018, 171(5): 897-926.

DOI：10.1007/s10955-018-2048-3

• Higher order nonlinear Schrodinger equation
• Averaging principle
• Strong convergence
• Fast-slow stochastic partial differential equation

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrodinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrodinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrodinger equation with a modified coefficient.

• 出版日期2018-6
• 单位东北师范大学