
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
Abstract:
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.

