FROM-PDE

Frobenius Manifolds and Hamiltonian Partial Differential Equations

Coordinatore	SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Italy [IT]
Totale costo	864˙000 €
EC contributo	864˙000 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2008-AdG
Funding Scheme	ERC-AG
Anno di inizio	2009
Periodo (anno-mese-giorno)	2009-01-01   -   2013-12-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI  Organization address address: VIA BONOMEA 265 city: TRIESTE postcode: 34136 contact info Titolo: Mr. Nome: Luca Cognome: Bardi Email: send email Telefono: 390404000000 Fax: 390404000000	IT (TRIESTE)	hostInstitution	864˙000.00
2	SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI  Organization address address: VIA BONOMEA 265 city: TRIESTE postcode: 34136 contact info Titolo: Prof. Nome: Boris Cognome: Dubrovin Email: send email Telefono: 390404000000 Fax: 390404000000	IT (TRIESTE)	hostInstitution	864˙000.00

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 Obiettivo del progetto (Objective)

'The basic idea of the project is to apply methods and results of the theory of integrable systems to non-integrable PDEs. We do not promise to solve any PDE; however, in certain strongly nonlinear regimes, solutions to a conservative non-integrable PDE exhibit integrable behaviour. The realization of this idea, supported by some preliminary analytical and numerical results, will consist of three main tasks: 1) classify normal forms of quasilinear Hamiltonian PDEs and their perturbations; 2) reduce the lists of asymptotic solutions to an abridged list of universal forms represented via Painlevé transcendents, theta-functions, etc.; 3) establish matching rules between the universal asymptotic expansions. Differential-geometric methods based on the theory of Frobenius manifolds will be crucial in solving the classification problems; analytic and algebro-geometric techniques applied to the Hurwitz spaces of Riemann surfaces will be instrumental in the description of nonlinear oscillatory regimes; selected solutions to Painlevé equations and their generalizations will be needed for the analytic description of transitions from regular to oscillatory behaviour. The project is aiming at creation of an online library of the main qualitative types of behaviour of solutions to large classes of nonlinear evolutionary PDEs supplied with analytic expressions, numerical codes and visualization tools, as well as with tests of existence of a Hamiltonian structure, integrability or almost integrability. Such a library will both stimulate the research in the field and lead to a high visibility of the project.'