Integrable Hamiltonian Hierarchies: Spectral and Geometric Methods (Lecture Notes in Physics, 748, Band 747) - Hardcover

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

Hardcover

ISBN 10: 3540770534 ISBN 13: 9783540770534

Verlag: Springer, 2008

Inhaltsangabe

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.

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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 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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 3540770534
• ISBN 13: 9783540770534
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 655
• Kontakt zum Hersteller: GPSR Kontakt; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Deutschland