Integrable Hamiltonian Hierarchies Spectral and Geometric Methods /

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 equ...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Gerdjikov, Vladimir (Autor), Vilasi, Gaetano (Autor), Yanovski, Alexandar Borisov (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008.
Edición:1st ed. 2008.
Colección:Lecture Notes in Physics, 748
Temas:
Mathematical physics.
Mathematical analysis.
Geometry.
Physics.
Astronomy.
Mathematical Methods in Physics.
Analysis.
Theoretical, Mathematical and Computational Physics.
Physics and Astronomy.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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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