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UID:30462
DTSTAMP:20190724T045459Z
SUMMARY:Mathematical Physics & Integrable Systems seminar: Jeremy Schiff (Bar-Ilan University, Israel)
LOCATION:Sibson Lecture Theatre 2 (SIBLT2), Sibson Building
DESCRIPTION:Abstract\nThere is an algorithmic procedure to find the infinitesimal symmetries of a given PDE, but "exponentiating" these to find formulas for finite symmetries is usually not possible. Bäcklund transformations are a wide class of methods, that exist for many special PDEs, to construct new solutions from old ones; however they typically do not involve continuous deformations and thus it is not immediately clear how to use them to derive standard, infinitesimal, symmetries. We describe the hidden way in which Bäcklund transformations generate infinitesimal symmetries of equations such as Korteweg-de Vries, Camassa-Holm, Boussinesq and Degasperis-Procesi. Using Bäcklund transformations gives a quick and simple proof of the existence of an infinite number of commuting infinitesimal local symmetries for these equations, a derivation of the standard recursion formulae with no issues of locality, and some explicit formulas for nonlocal, noncommuting symmetries. The nonlinear superposition principle for Bäcklund transformations plays a critical role. However, for equations such as Boussinesq and Degasperis-Procesi, which are associated with 3rd order Lax pairs, the relevant superposition principles are new formulae describing the superposition of three Bäcklund transformations. We explain the Lie theoretic basis for this.\n\n
DTSTART:20180208T120000Z
DTEND:20180208T130000Z
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