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Invariant Measures for Stochastic Nonlinear Schrödinger Equations: Numerical Approximations and Symplectic Structures de Jialin Hong

Invariant Measures for Stochastic Nonlinear Schrödinger Equations: Numerical Approximations and Symplectic Structures: Lecture Notes in Mathematics, cartea 2251

Autor Jialin Hong, Xu Wang
en Limba Engleză Paperback – 23 aug 2019
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.
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Specificații

ISBN-13: 9789813290686
ISBN-10: 9813290684
Pagini: 220
Ilustrații: XIV, 220 p. 14 illus., 13 illus. in color.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.34 kg
Ediția:1st ed. 2019
Editura: Springer Nature Singapore
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Singapore, Singapore

Cuprins

Invariant measures and ergodicity.- Invariant measures for stochastic differential equations.- Invariant measures for stochastic nonlinear Schrödinger equations.- Geometric structures and numerical schemes for nonlinear Schrödinger equations.- Numerical invariant measures for damped stochastic nonlinear Schrödinger equations.- Approximation of ergodic limit for conservative stochastic nonlinear Schrödinger equations.

Notă biografică

Prof. Jialin Hong, professor, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China/School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China Dr. Xu Wang, Golomb visiting assistant professor, Department of Mathematics, Purdue University, West Lafayette, 47906 IN, USA.

Textul de pe ultima copertă

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.

Caracteristici

Gives a detailed introduction to ergodicity and symplectic and multi-symplectic structures for stochastic nonlinear Schrödinger equations Provides the study of ergodic numerical approximations for stochastic nonlinear Schrödinger equations without strong dissipative terms Constructs numerical approximations which inherit both dynamical behaviors and geometric structures even for stochastic nonlinear Schrödinger equation of conservative type