Mathematical Physics Studies

Darboux Transformations in Integrable Systems

Theory and their Applications to Geometry

Authors: Gu, Chaohao, Hu, Anning, Zhou, Zixiang

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Hardcover $189.00
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About this book

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry.

This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years.

Audience:

The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics.

Reviews

From the reviews:

"The book is concerned with mutual relations between the differential geometry of surfaces and the theory of integrable nonlinear systems of partial differential equations. It concentrates on the Darboux matrix method for constructing explicit solutions to various integrable nonlinear PDEs. … This book can be recommended for students and researchers who are interested in a differential-geometric approach to integrable nonlinear PDE’s." (Jun-ichi Inoguchi, Mathematical Reviews, Issue 2006 i)


Table of contents (7 chapters)

  • 1+1 Dimensional Integrable Systems

    Gu, Chaohao (et al.)

    Pages 1-64

  • 2+1 Dimensional Integrable Systems

    Gu, Chaohao (et al.)

    Pages 65-101

  • N + 1 Dimensional Integrable Systems

    Gu, Chaohao (et al.)

    Pages 103-120

  • Surfaces of Constant Curvature, Bäcklund Congruences and Darboux Transformation

    Gu, Chaohao (et al.)

    Pages 121-187

  • Darboux Transformation and Harmonic Map

    Gu, Chaohao (et al.)

    Pages 189-235

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4020-3088-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-1-4020-3087-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-90-481-6788-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Darboux Transformations in Integrable Systems
Book Subtitle
Theory and their Applications to Geometry
Authors
Series Title
Mathematical Physics Studies
Series Volume
26
Copyright
2005
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-3088-8
DOI
10.1007/1-4020-3088-6
Hardcover ISBN
978-1-4020-3087-1
Softcover ISBN
978-90-481-6788-3
Series ISSN
0921-3767
Edition Number
1
Number of Pages
X, 308
Topics