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Integrable Hamiltonian hierarchies : spectral and geometric methods

Author: V S Gerdjikov; Gaetano Vilasi; A B Yanovski
Publisher: Berlin : Springer, ©2008.
Series: Lecture notes in physics, 748.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This text 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 hierarchies.
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Document Type: Book
All Authors / Contributors: V S Gerdjikov; Gaetano Vilasi; A B Yanovski
ISBN: 9783540770534 3540770534 9783540770541 3540770542
OCLC Number: 213114127
Description: xii, 643 pages ; 25 cm.
Contents: Integrable Hamiltonian Hierarchies: Spectral Methods.- The Lax Representation and the AKNS Approach.- The Direct Scattering Problem for theZakharov-Shabat System.- The Inverse Scattering Problem for the Zakharov-Shabat System.- The Generalized Fourier Transforms.- Fundamental Properties of the solvable NLEEs.- Hierarchies of Hamiltonian structures.- The NLEEs and the Gauge Transformations.- The Classical r-Matrix Method.- Integrable Hamiltonian Hierarchies: Geometric Theory of the Recursion Operators.- Smooth Manifolds.- Hamiltonian Dynamics.- Vector-Valued Differential Forms.- Integrability and Nijenhuis Tensors.- Poisson-Nijenhuis structures Related to the Generalized Zakharov-Shabat System.- Linear Bundles of Lie Algebras and Compatible Poisson Structures.
Series Title: Lecture notes in physics, 748.
Responsibility: V.S. Gerdjikov, G. Vilasi, A.B. Yanovski.

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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  Read more...

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