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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...
We consider a special kind of Lie algebra extension, called ''universal'' extension, introduced recently. We show that there is one-to-one correspondence with commutative associative algebras. We also investigate the Casimir invariants for the ''universal'' extensions and consider in detail the so-called coextension structures, arising in the calculation of the Casimir functions.
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