TheAdvancedResearchWorkshop NewTrendsinIntegrabilityandPartial Solvability (ARW. 978791) tookplaceinthebeautifulsettingoftheFaculty ofMedicineofC adizUniversity smainroomonJune13 15,2002. Although thenumberofparticipantswas 30, thelectureswereattendedbymorethan one hundred researchers from around the world who were also attending the NEEDS 2002 meeting. Theaim of the organizers was to take advantage of these events to bring together researchers from the ?eld of integrable systems and/or from the particular subject of partial integrability, in view of the current interest in combining methods and ideas arising from both areas. A widevariety of topics were covered in the talks andthe subsequent discussions, including the analysis of reductions and solutions of integrable nonlinear partial di?erential equations and dynamical systems, new me- ods for the analysis of initial-boundary value problems for linear partial di?erential equations, quasi-exactly solvable Bose systems, the geometric theory of ordinarydi?erential equations, exactly and partially solvable spin models, the theory of nonlocal symmetries of di?erential equations, and superintegrable systems. Theworkshop revealed the growing importance of the theory of integrable system as well as the emerging theory of partially solvable systems. The present volume contains a series of invited contributions describing the background and recent developments of the main subjects discussed in the workshop. Special emphasis has been laid on providing self-contained and detailed presentations of the theory. M. J. Ablowitz and J. Villarroel give a detailed description of the inverse scattering for the KP equation, a keystone in the theory of integrable s- tems.

Klappentext
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. TOC:Preface.- List of Contributors.- Initial value problems and solutions of the Kadomtsev-Petviashvili equation.- Partially superintegrable (indeed isochronous) systems are not rare.- Initial-boundary value problems for linear PDEs: the analyticity approach.- Quasi-exactly solvable Bose systems.- The Riemann and Einstein-Weyl geometries in the theory of ordinary differential equations, their applications and all that.- Dunkl operators and Calogero-Sutherland models.- Yang-Baxter maps and matrix solitons.- Nonlocal Symmetries and Ghosts.- Integrable BCN analytic difference operators: hidden parameter symmetries and eigenfunctions.- On the prolongation of a hierarchy of hydrodynamic chains.- Superintegrable systems in classical and quantum mechanics.

Zusammenfassung
Proceedings of the NATO Advanced Research Workshop, held in Cadiz, Spain, from 12 to 16 June 2002

Inhalt
Initial value problems and solutions of the Kadomtsev-Petviashvili equation.- Partially superintegrable (indeed isochronous) systems are not rare.- Initial-boundary value problems for linear PDEs: the analyticity approach.- Quasi-exactly solvable Bose systems.- The Riemann and Einstein-Weyl geometries in the theory of ordinary differential equations, their applications and all that.- Dunkl operators and Calogero-Sutherland models.- Yang-Baxter maps and matrix solitons.- Nonlocal Symmetries and Ghosts.- Integrable BCN analytic difference operators: hidden parameter symmetries and eigenfunctions.- On the prolongation of a hierarchy of hydrodynamic chains.- Superintegrable systems in classical and quantum mechanics.