Bäcklund Transformations for Equations of Sine-Gordon Type
Thomas Ivey
Department of Mathematics visiting scholar, University of Colorado Boulder
Date and time:
Tuesday, October 22, 2013 - 4:00pm
Location:
ECOT 226
Abstract:
A geometric formulation of Bäcklund transformations between wavelike Monge-Ampere equations (for one function of two variables) leads to an overdetermined PDE system for the equations defining the transformation. This system becomes more manageable when the transformations are assumed to be quasilinear and autonomous. I'll discuss our results on classifying Bäcklund transformations of this type; besides the sine-Gordon equation itself, other nonlinear PDEs that appear include Darboux-integrable equations such as Liouville's equation and $u_{xy} = u_x e^u$.
This is joint work with Jeanne Clelland (CU Math).