New Trends in Integrability and Partial Solvability. Questo articolo non è disponibile.New Trends in Integrability and Partial Solvability

This book contains discussions of some of the most exciting subjects in the intimately related fields of integrability and partial solvability. It presents a wide variety of advanced topics, such as the symmetry approach to integrability and partial solvability, partially and exactly solvable many-body systems, the interplay between chaos and integrability, the inverse scattering method for initial-boundary problems, and new methods for dealing with reductions and deformations of integrable systems. A special effort is made to discuss the present frontiers of the concept of integrability. The articles cover some of the most active areas in integrability and partial and exact solvability. More precisely, the following topics are discussed: nonlinear harmonic oscillators, chaotic dynamics, initial-boundary nonlinear problems, reductions and deformations of integrable systems, Darboux transformations, Yang-Baxter equations and matrix solitons, superintegrable systems, exactly and quasi-exactly solvable spin and many-body models.

Preface. List of Contributors. Initial value problems and solutions of the Kadomtsev-Petviashvili equation; M.J. Ablowitz, J. Villarroel. Partially superintegrable (indeed isochronous) systems are not rare; F. Calogero. Initial-boundary value problems for linear PDEs: the analyticity approach; A. Degasperis, S.V. Manakov, P.M. Santini. Quasi-exactly solvable Bose systems; S.N. Dolya, O.B. Zaslavskii. The Riemann and Einstein-Weyl geometries in the theory of ordinary differential equations, their applications and all that; V. Dryuma. Dunkl operators and Calogero-Sutherland models; F. Finkel, et al. Yang-Baxter maps and matrix solitons; V.M. Goncharenko, A.P. Veselov. Nonlocal Symmetries and Ghosts; P.J. Olver. Integrable BCN analytic difference operators: hidden parameter symmetries and eigenfunctions; S.N.M. Ruijsenaars. On the prolongation of a hierarchy of hydrodynamic chains; A.B. Shabat, L. Martínez Alonso. Superintegrable systems in classical and quantum mechanics; P. Winternitz.