Global solutions of stochastic nonlinear Schr\"odinger system with quadratic interaction
Analysis of PDEs
2023-05-30 v2 Probability
Abstract
The time-global existence of solutions to a system of stochastic Schr\"odinger equations with multiplicative noise and the quadratic nonlinear terms are discussed in this paper. The same system in the deterministic treatment was studied in [18] where the mass and energy are conserved. In our stochastic situation, those are not conserved and which causes several difficulties in the arguments of composing a-priori estimate.
Keywords
Cite
@article{arxiv.2301.06659,
title = {Global solutions of stochastic nonlinear Schr\"odinger system with quadratic interaction},
author = {Masaru Hamano and Shunya Hashimoto and Shuji Machihara},
journal= {arXiv preprint arXiv:2301.06659},
year = {2023}
}
Comments
28 pages, no figures