Modern Birkhäuser Classics

Ginzburg-Landau Vortices

Authors: Bethuel, Fabrice, Brezis, Haim, Helein, Frederic

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  • Affordable, softcover reprint of a classic textbook
  • Authors are well-known specialists in nonlinear functional analysis and partial differential equations
  • Written in a clear, readable style with many examples
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eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-66673-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-66672-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small.  Thus, it is of great interest to study the asymptotics as ɛ tends to zero.

One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized.

The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis, partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-66673-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-66672-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Ginzburg-Landau Vortices
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2017
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-66673-0
DOI
10.1007/978-3-319-66673-0
Softcover ISBN
978-3-319-66672-3
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XXIX, 159
Number of Illustrations
4 b/w illustrations, 1 illustrations in colour
Topics