Obiettivo In the past decade the theory of discrete integrable systems described by difference equations has emerged as the most prominent direction of research within the field of integrability. The study of difference equations constituting the exact analogues of integrable differential equations have fundamentally contributed to mathematics by opening new fields of research, e.g. in difference geometry and the theory of non-linear special functions.This proposal concerns both linear difference equations that possess a class of Darboux symmetry transformations and non-linear difference equations that are compatibility conditions for a set of the linear equations. Whilst most of the activity in the field has concentrated on equations of hyperbolic type, the emphasis of the proposal lies in the study of equations of elliptic type, which forms almost unchartered territory, although importantly first paradigms in this direction has been constructed by the applicant. The structure of integrable difference equations of the latter type is expected to be richer, and thus more fundamental, than of their continuous counterparts, and this will form the principal object of investigation.In particular, this project endeavours to find discrete (difference) integrable analogues of the equations that describe:i) Axisymmetric, stationary, vacuum Einstein fields (Ernst equation),ii) stationary, vacuum Einstein-Maxwell fields (Ernst-Maxwell-Weyl equations), both through the consideration of auto-Backlund and Darboux transformations.An important problem is the question of classification of such systems. Experience with discrete systems suggests that this problem is tractable and can be formulated in a precise way. To resolve this problem the theory of reductions of discrete integrable systems will be further developed. An aim is to gain insight in integrable reductions of Einstein's equations of General Relativity, using discrete Ernst equations as toy model of discrete gravity. Campo scientifico natural sciencesphysical sciencesrelativistic mechanicsnatural sciencesphysical sciencesastronomyobservational astronomygravitational wavesnatural sciencescomputer and information sciencesnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Parole chiave Difference Equations Discrete Geometry Ernst Type Equations Integrable Systems Programma(i) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Argomento(i) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Invito a presentare proposte FP6-2002-MOBILITY-5 Vedi altri progetti per questo bando Meccanismo di finanziamento EIF - Marie Curie actions-Intra-European Fellowships Coordinatore UNIVERSITY OF LEEDS Contributo UE Nessun dato Indirizzo Woodhouse Lane LEEDS Regno Unito Mostra sulla mappa Collegamenti Sito web Opens in new window Costo totale Nessun dato
