Events Calendar
Feb 8
12:00 - 13:00
Mathematical Physics & Integrable Systems seminar: Jeremy Schiff (Bar-Ilan University, Israel)
SMSAS Mathematical Physics seminars
Bäcklund Transformations and Infinitesimal Symmetries


There 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.


Sibson Lecture Theatre 2 (SIBLT2),
Sibson Building
United Kingdom


Open to All interested persons,

Contact: Dr Pavlos Xenitidis
School of Mathematics, Statistics and Actuarial Science


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Last Updated: 10/01/2012