Abstract
Jeanne Clelland
University of Colorado at Boulder
Title: Backlund transformations of hyperbolic Monge-Ampere equations
Abstract: Backlund transformations provide a method for contructing new
solutions of a partial differential equation from a known solution. The
new solutions are constructed by solving ordinary differential equations.
These transformations are known to exist for certain special PDEs - in
particular, for most soliton equations - but it is not known what
conditions a PDE must satisfy in order to have a Backlund transformation.
In this talk I will describe some classical Backlund transformations of
hyperbolic Monge-Ampere equations in terms of exterior differential
systems. Using Cartan's method of equivalence we can classify the
homogenous examples, i.e., those transformations having maximal symmetry.
In the process, we discover a previusly unknown Backlund transformation
between timelike surfaces of constant mean curvature in R^{1,2}.
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