Stochastic Nonlinear Equations of Schrödinger Type

Abstract

In this article, the solution for a stochastic nonlinear equation of Schrödinger type, which is perturbed by an infinite dimensional Wiener process, is investigated. The existence of the solution is proved by using the Galerkin method. Moment estimates for the solution are also derived. Examples from physics are given in the final part of the article.

Keywords:

• Galerkin method
• Infinite dimensional Wiener process
• Nonlinear stochastic Schrödinger equations

Mathematics Subject Classification:

• 60H15
• 35Q41
• 81Q05

Acknowledgments

This work was supported by CNCSIS-UEFISCSU (Romania) project number PNII IDEI ID 2162/nr. 501/2008 and by Deutsche Forschungsgemeinschaft (Germany) project GR 1525/10-1.

Notes

We denote by C _HV the embedding constant of H↪V.