Integrable Hamiltonian Hierarchies: Spectral and Geometric Methods [Paperback]

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 hierarchies.

Integrable Hamiltonian Hierarchies: Spectral Methods.- The Lax Representation and the AKNS Approach.- The Direct Scattering Problem for theZakharovShabat System.- The Inverse Scattering Problem for the ZakharovShabat 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.- PoissonNijenhuis structures Related to the Generalized ZakharovShabat System.- Linear Bundles of Lie Algebras and Compatible Poisson Structures.

From the reviews:

The book under review provides a wide overview on the so-called soliton equations & . the book contains many topics that experts will find interesting, it is well organized and is an excellent research monograph on soliton equations. & it is accessible to a wide range of readers, from the experts in the field, to researchers who are interested in nonlinear evolution equations and PhD students who would like to learn more about this field. (A. Yoshioka, Il Nuovo Saggiatore, Vol. 29 (5-6), 2013)

Will be of great use to anybody who is interested in the AKNS method & . The bibliographic remarks given at the end of each section are quite useful if one wants to be oriented in the existing trends of the theory. & succeeded in bringing together different approaches while keeping the main focus on Recursion Operators. & It should be mentioned that the book is written in a reader-friendly way & . recommended to PhD students who want to llcv