Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Bi-linear algebraic systems - how they arise and how to approach them
Thomas Wolf, Brock University
Friday, September 12, 2003, at U. of Waterloo.


If a *given* non-linear differential equation (DE) or system of DEs is to be investigated wrt. special properties, like infinitesimal symmetries, then the resulting conditions (e.g. for the generators of these symmetries) are linear. If, on the other hand, one wants to *find* PDEs which obey higher order symmetries (as a pre-requisite for being integrable) then one searches for 2 things at once: DEs and symmetries and the resulting conditions become non-linear. In the simplest case these are bi-linear algebraic systems but they can become large: >1000 equations for >200 unknowns.

In the talk motivating applications are shown, methods towards the solution of these systems are explained and recent results are presented. Emphasis will be put on a technique to merge special solutions into fewer, more general solutions through re-prarametrization.


Last modified on Sunday, 04 November 2012, at 15:42 hours.