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Physical Sciences and Mathematics Commons

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Utah State University

Mathematics and Statistics Faculty Presentations

2011

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Full-Text Articles in Physical Sciences and Mathematics

Darboux Integrability - A Brief Historial Survey, Ian M. Anderson May 2011

Darboux Integrability - A Brief Historial Survey, Ian M. Anderson

Mathematics and Statistics Faculty Presentations

No abstract provided.


B ̈Acklund Transformations For Darboux Integrable Equations, Ian M. Anderson Jan 2011

B ̈Acklund Transformations For Darboux Integrable Equations, Ian M. Anderson

Mathematics and Statistics Faculty Presentations

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 …