New Trends in Integrability and Partial Solvability

by Shabat, A. B.; Gonzalez-Lopez, A.; Manas, M.; Alonso, L. Martinez; Rodriguez, M. A.

• ISBN13: 9781402018350
• ISBN10: 1402018355
• Format: Hardcover
• Copyright: 2004-02-01
• Publisher: Kluwer Academic Pub

Summary

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.

Table of Contents

Preface	vii
List of Contributors	xi
M.J. Ablowitz and J. Villarroel
Initial value problems and solutions of the Kadomtsev-Petviashvili equation	1	(18)
F. Calogero
Partially superintegrable (indeed isochronous) systems are not rare	19	(60)
A. Degasperis, S.V. Manakov, P.M. Santini
Initial-boundary value problems for linear PDEs: the analyticity approach	79	(26)
S.N. Dolya and O.B. Zaslavskii
Quasi-exactly solvable Bose systems	105	(10)
V. Dryuma
The Riemann and Einstein-Weyl geometries in the theory of ordinary differential equations, their applications and all that	115	(42)
F. Finkel et al.
Dunkl operators and Calogero-Sutherland models	157	(34)
V.M. Goncharenko and A.P. Veselov
Yang-Baxter maps and matrix solitons	191	(8)
P.J. Olver
Nonlocal Symmetries and Ghosts	199	(18)
S.N.M. Ruijsenaars
Integrable BCjy analytic difference operators: hidden parameter symmetries and eigenfunctions	217	(46)
A.B. Shabat and L. Martinez Alonso
On the prolongation of a hierarchy of hydrodynamic chains	263	(18)
P. Winternitz
Superintegrable systems in classical and quantum mechanics	281