New Trends in Integrability and Partial Solvability

A B Shabat

ISBN 10: 1402018355 / ISBN 13: 9781402018350

Editore: Springer Jan 2004, 2004

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Neuware - 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.

Codice articolo 9781402018350

Dati bibliografici

• Titolo: New Trends in Integrability and Partial Solvability
• Editore: Springer Jan 2004
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 1402018355
• ISBN 13: 9781402018350
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 247 L x 168 A x 21 P (millimetri) 247 millimetri di larghezza per 168 millimetri di altezza per 21 millimetri di profondità
• Peso: 608 grammi

Descrizione articolo

Riassunto

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.

Contenuti

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.