Document Type
Presentation
Journal/Book Title/Conference
Differential Geometry and Tanaka Theory, Research Institute for Mathematical Sciences, Kyoto University, January 24--28
Publication Date
1-24-2011
Abstract
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.
Recommended Citation
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.
Comments
Presentation given for the Research Institute for Mathematical Sciences, Kyoto University, January 24--28, 2011. Presentation available for download through link above.