This book provides some recent advance in the study of shastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for shastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for shastic nonlinear Schrödinger equations.
This book will appeal to researchers who are interested in numerical analysis, shastic analysis, ergodic theory, partial differential equation theory, etc.