Invariant Measures for Stochastic Nonlinear Schrödinger Equations Numerical Approximations and Symplectic Structures /

• Main Authors: Hong, Jialin (Author, http://id.loc.gov/vocabulary/relators/aut), Wang, Xu (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Lecture Notes in Mathematics, 2251
• Subjects: Probabilities.; Numerical analysis.; Dynamics.; Ergodic theory.; Partial differential equations.; Probability Theory and Stochastic Processes.; Numerical Analysis.; Dynamical Systems and Ergodic Theory.; Partial Differential Equations.
• Physical Description: XIV, 220 p. 14 illus., 13 illus. in color. online resource.
• ISBN: 9789813290693
• ISSN: 0075-8434 ;
• DOI: 10.1007/978-981-32-9069-3

This book provides some recent advance in the study of stochastic 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 stochastic 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 stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.