
Symmetry in Nonlinear Mathematical Physics  2009
Oleg Morozov (Moscow State Technical University of Civil Aviation, Russia)
Coverings of differential equations and Lie pseudogroups
Abstract:
Coverings, also known as Lax pairs, WahlquistEstabrook prolongation structures, or zerocurvature representations, are a convenient framework for dealing with nonlocal symmetries and conservation laws, inverse scattering transformations, Bäcklund transformations,
recursion operators, and deformations of nonlinear partial differential equations. Consequently, the problem of recognizing whether a given PDE has a covering is of great importance. I will talk about one of the possible approaches to solution which use Élie Cartan's structure theory of Lie pseudogroups. Examples will include new coverings for the rth modified dispersionless KP equation, the rth dispersionless (2+1) Dym equation and the deformed BoyerFinley equation.

