Integrable Hamiltonian Hierarchies: Spectral and Geometric Methods: 748 (Lecture Notes in Physics, 748) - Hardcover

Gerdjikov, Vladimir; Vilasi, Gaetano; Yanovski, Alexandar Borisov

Hardcover

ISBN 10: 3540770534 ISBN 13: 9783540770534

Publisher: Springer, 2008

Synopsis

In the past decades now a famous class of evolution equations has been discovered and intensively studied, a class including the nowadays celebrated Korteweg-de Vries equation, sine-Gordon equation, nonlinear Schr. odinger equation, etc. The equations from this class are known also as the soliton equations or equations solvable by the so- called Inverse Scattering Tra- form Method. They possess a number of interesting properties, probably the most interesting from the geometric point of view of being that most of them are Liouville integrable Hamiltonian systems. Because of the importance of the soliton equations, a dozen monographs have been devoted to them. H- ever, the great variety of approaches to the soliton equations has led to the paradoxical situation that specialists in the same ?eld sometimes understand eachotherwithdi?culties. Wediscovereditourselvesseveralyearsagoduring a number of discussions the three of us had. Even though by friendship binds us, we could not collaborate as well as we wanted to, since our individual approach to the ?eld of integrable systems (?nite and in?nite dimensional) is quite di?erent. We have become aware that things natural in one approach are di?cult to understand for people using other approaches, though the - jects are the same, in our case - the Recursion (generating) Operators and theirapplicationsto?niteandin?nitedimensional(notnecessarilyintegrable) Hamiltonian systems.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2008
• Language: English
• ISBN 10: 3540770534
• ISBN 13: 9783540770534
• Binding: Hardcover
• Number of pages: 655