Journal of statistical physics, 2018-06, Vol.171 (5), p.897-926
This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger 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 Schrödinger 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 Schrödinger equation with a modified coefficient.
Strong convergence ; Higher order nonlinear Schrödinger equation ; Theoretical, Mathematical and Computational Physics ; Quantum Physics ; 35Q53 ; Averaging principle ; 70K65 ; Physics ; Fast–slow stochastic partial differential equation ; Statistical Physics and Dynamical Systems ; Physical Chemistry ; 70K70 ; 60H15 ; Diffusion rate ; Qualitative analysis ; Schroedinger equation ; Partial differential equations ; RANDOMNESS ; MATHEMATICAL SOLUTIONS ; DIFFUSION EQUATIONS ; STOCHASTIC PROCESSES ; NONLINEAR PROBLEMS ; SCHROEDINGER EQUATION ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; CONVERGENCE ; DYNAMICAL SYSTEMS ; OSCILLATIONS
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