Integrable Hamiltonian Hierarchies : Spectral and Geometric Methods

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.