New Trends in Integrability and Partial Solvability

ISBN-13: 9781402018350 / Angielski / Twarda / 2004 / 297 str.

A. B. Shabat; A. Gonzalez-Lipez; M. Manas

Opis

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.

Spis treści

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.