Special Session 19: Stochastic Partial Differential Equations

Multi solitary waves to stochastic nonlinear Schroedinger equations

Deng Zhang
Shanghai Jiao Tong University
Peoples Rep of China
Co-Author(s):    Michael Roeckner, Yiming Su, Deng Zhang
In this talk we will present the recent work on the multi solitary waves to stochastic nonlinear Schroedinger equations driven by linear multiplicative noise, in both the mass-critical and subcritical cases. Unlike in the deterministic case, the existence of stochastic multi-solitons cannot be obtained from that of stochastic multi-bubble blow-up solutions, due to the absence of pseudo-conformal invariance. We present a constructive proof by utilizing the rescaling approach and the modulation method. The constructed multi-solitons behave asymptotically as a sum of finitely many solitary waves, and the convergence rate of the remainders can be of either exponential or polynomial type, which reflects the effects of noise on the asymptotical behavior of solutions.