In this talk I will review some recent results on multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schrödinger equations. We will show the corresponding construction and conditional uniqueness results, which provide new examples for the mass quantization conjecture and the soliton resolution conjecture. Furthermore, in the very low asymptotic regime, the refined uniqueness is obtained in the deterministic case. At last, we show the direct construction of stochastic multi-solitons in the mass critical and subcritical cases, especially in the absence of the pseudo-conformal symmetry.
Deng Zhang is an associate professor at Shanghai Jiao Tong University. He obtained his PhD degree in 2014 from Chinese Academy of Sciences and Bielefeld University, under the supervision of Prof. Zhi-Ming Ma and Prof. Michael Röckner. His research focuses on stochastic partial differential equations, in particular stochastic Schrödinger equations and stochastic fluid equations.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai