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Lecture Notes in Mathematics

Invariant Measures for Stochastic Nonlinear Schrödinger Equations

Numerical Approximations and Symplectic Structures

Authors: Hong, Jialin, Wang, Xu

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  • 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
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  • ISBN 978-981-329-069-3
  • Digitally watermarked, DRM-free
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About this book

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.

About the authors

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.

Table of contents (6 chapters)

Table of contents (6 chapters)
  • Invariant Measures and Ergodicity

    Pages 1-29

    Hong, Jialin (et al.)

  • Invariant Measures for Stochastic Differential Equations

    Pages 31-61

    Hong, Jialin (et al.)

  • Invariant Measures for Stochastic Nonlinear Schrödinger Equations

    Pages 63-79

    Hong, Jialin (et al.)

  • Geometric Structures and Numerical Schemes for Nonlinear Schrödinger Equations

    Pages 81-108

    Hong, Jialin (et al.)

  • Numerical Invariant Measures for Damped Stochastic Nonlinear Schrödinger Equations

    Pages 109-152

    Hong, Jialin (et al.)

Buy this book

eBook n/a
  • ISBN 978-981-329-069-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-981-329-068-6
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Invariant Measures for Stochastic Nonlinear Schrödinger Equations
Book Subtitle
Numerical Approximations and Symplectic Structures
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2251
Copyright
2019
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-329-069-3
DOI
10.1007/978-981-32-9069-3
Softcover ISBN
978-981-329-068-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 220
Number of Illustrations
1 b/w illustrations, 13 illustrations in colour
Topics