Title of article :
Global and Local Solutions of Stochastic Nonlinear Schrödinger System With Quadratic Interaction
Author/Authors :
Hamano ، Masaru Department of Mathematics - Faculty of Science and Engineering - Waseda University , Hashimoto ، Shunya Department of Mathematics - Faculty of Science - Saitama University , Machihara ، Shuji Department of Mathematics - Faculty of Science - Saitama University
Abstract :
Global and local existence results for the solutions of systems of stochastic Schr\ odinger equations with multiplicative noise and quadratic nonlinear terms are discussed in this paper. The same system in the deterministic treatment was studied in[Hayashi, N., Ozawa, T., Tanaka, K.: On a system of nonlinear Schrödinger equations with quadratic interaction. Ann. I. H. Poincaré 30, 661–690 (2013)] where the mass and energy are conserved. In our stochastic situation, those are not conserved.
Keywords :
Stochastic nonlinear Schrödinger system , Quadratic interaction , Global existence
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
