Differential Geometry and Tanaka Theory, Research Institute for Mathematical Sciences, Kyoto University, January 24--28
Lie symmetry reduction is typically viewed as an integration method for differential systems of finite type, that is, systems of ordinary differential equations.
In this talk I shall present two new, recent applications of Lie symmetry reduction to the study of partial differential equations.
The first gives a remarkably simple method for constructing B ̈acklund transformations.
The second also gives a simple, very general method for constructing Darboux integrable equations.
The combination of these result in a new method for constructing B ̈acklund transformations for Darboux integrable equations.
The utility of this group theoretic approach will be illustrated by a variety of novel examples.
Anderson, I. (2011, January 24). B"acklund Transformations for Darboux Integrable Equations. Presented at the Differential Geometry and Tanaka Theory, Research Institute for Mathematical Sciences, Kyoto University.