Lecture Notes in Physics

Integrable Hamiltonian Hierarchies

Spectral and Geometric Methods

Authors: Gerdjikov, Vladimir, Vilasi, Gaetano, Yanovski, Alexandar Borisov

  • The only detailed presentation of the recursion operators both from geometric and spectral theory viewpoint

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eBook 107,09 €
price for Korea, Republic of (South Korea) (gross)
  • ISBN 978-3-540-77054-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 129,99 €
price for Korea, Republic of (South Korea) (gross)
  • ISBN 978-3-540-77053-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 129,99 €
price for Korea, Republic of (South Korea) (gross)
만료일 November 5, 2017
  • ISBN 978-3-642-09577-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform.

The book brings together the spectral and the geometric approaches and as such
will be useful to a wide readership: from researchers in the field of nonlinear
completely integrable evolution equations to graduate and post-graduate students.

Reviews

From the reviews:

“The book under review provides a wide overview on the so-called soliton equations … . the book contains many topics that experts will find interesting, it is well organized and is an excellent research monograph on soliton equations. … it is accessible to a wide range of readers, from the experts in the field, to researchers who are interested in nonlinear evolution equations and PhD students who would like to learn more about this field.” (A. Yoshioka, Il Nuovo Saggiatore, Vol. 29 (5-6), 2013)

“Will be of great use to anybody who is interested in the AKNS method … . The bibliographic remarks given at the end of each section are quite useful if one wants to be oriented in the existing trends of the theory. … succeeded in bringing together different approaches while keeping the main focus on Recursion Operators. … It should be mentioned that the book is written in a reader-friendly way … . recommended to PhD students who want to learn more about the subject.” (Giuseppe Marmo, Bulletin of the London Mathematical Society, Vol. 44, 2012)

“This is a book on integrable partial differential equations. … scope of this book is large. It is a reference book. It can serve as an advance graduate textbook. … A signal feature of this book is the number of references, allowing one to review and study other examples and related aspects. … Overall, this work is impressive in what it covers and is of value to students and researchers in this area.” (D. J. Kaup, Bulletin of the London Mathematical Society, December, 2009)

"This monograph aims to discuss about the inverse scattering transform and the bi-Hamiltonian theory of soliton equations in both analytical and geometric approaches. … The book is well organized and clearly written. … The interested readers … can easily find various relevant theories and their references. It is an excellent research monograph summarizing and evaluating our growing body of research on soliton theory and integrable Hamiltonian systems." (Ma Wen-Xiu, Zentralblatt MATH, Vol. 1167, 2009)

"The book under review is divided into two parts. … devoted to the recollection of many by-now classical results concerning the application of spectral methods to integrable Hamiltonian hierarchies. … The two parts are written with the intention of being understandable to nonspecialists in the field and are self-contained. Each chapter ends with a rich bibliographical review which emphasizes the contribution of the authors to the field." (Simonetta Abenda, Mathematical Reviews, Issue 2009 m)


Table of contents (16 chapters)

  • Introduction

    Gerdjikov, V.S. (et al.)

    Pages 3-36

    Preview Buy Chapter 24,95 €
  • The Lax Representation and the AKNS Approach

    Gerdjikov, V.S. (et al.)

    Pages 37-70

    Preview Buy Chapter 24,95 €
  • The Direct Scattering Problem for theZakharov–Shabat System

    Gerdjikov, V.S. (et al.)

    Pages 71-95

    Preview Buy Chapter 24,95 €
  • The Inverse Scattering Problem for the Zakharov–Shabat System

    Gerdjikov, V.S. (et al.)

    Pages 97-132

    Preview Buy Chapter 24,95 €
  • The Generalized Fourier Transforms

    Gerdjikov, V.S. (et al.)

    Pages 133-173

    Preview Buy Chapter 24,95 €

Buy this book

eBook 107,09 €
price for Korea, Republic of (South Korea) (gross)
  • ISBN 978-3-540-77054-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 129,99 €
price for Korea, Republic of (South Korea) (gross)
  • ISBN 978-3-540-77053-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 129,99 €
price for Korea, Republic of (South Korea) (gross)
만료일 November 5, 2017
  • ISBN 978-3-642-09577-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Integrable Hamiltonian Hierarchies
Book Subtitle
Spectral and Geometric Methods
Authors
Series Title
Lecture Notes in Physics
Series Volume
748
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-77054-1
DOI
10.1007/978-3-540-77054-1
Hardcover ISBN
978-3-540-77053-4
Softcover ISBN
978-3-642-09577-1
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XII, 643
Topics