Symmetry in Nonlinear Mathematical Physics - 2009

Alexei Cheviakov (University of Saskatchewan, Canada)

An extended procedure for finding exact solutions of PDEs arising from potential symmetries

Lie point symmetries and nonlocal symmetries of PDE systems are widely used for construction of exact invariant solutions. I will describe an extended algorithmic procedure that, for a given nonlocal (potential) symmetry, can yield additional exact solutions, which cannot be found using the usual algorithm.
As an example, I will present a tree of nonlocally related PDE systems for planar gas dynamics equations in the Lagrangian framework, a classification of its nonlocal symmetries for a particular constitutive function, and examples of new solutions obtained using the extended algorithm.