Introduction.- Lax Representation and AKNS Approach.- The Direct Scattering Problem.- The Inverse Scattering Problem.- The Generalized Fourier Transforms.- Fundamental Properties of the Solvable NLEEs.- Hierarchies of Hamiltonian Structures.- The NLEEs and Gauge Transformations.- The Classical R-Matrix Method.- Smooth Manifolds.- Hamiltonian Dynamics.- Vector-Valued Differential Forms.- Integrability and Nijenhuis Tensors.- Poisson-Nijenhuis Structures Related to GZS System.- Linear Bundles of Lie Algebras and Compatible Poisson Structures.
(source: Nielsen Book Data)
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. 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 post-graduate students. (source: Nielsen Book Data)