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Full-Text Articles in Physical Sciences and Mathematics
Darboux Integrability - A Brief Historial Survey, Ian M. Anderson
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
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 …