Symmetry in Nonlinear Mathematical Physics - 2009
Christodoulos Sophocleous and Christina Tsaousi (University of Cyprus, Nicosia, Cyprus)
Differential invariants for systems of linear hyperbolic equations
We consider a general class of systems of two linear hyperbolic equations. Motivated by the existence
of the Laplace invariants for the single linear hyperbolic equation, we adopt the problem of finding differential
invariants for the system. We derive the equivalence group of transformations for this class of systems. The
infinitesimal method, which makes use of the equivalence group, is employed for determining the desired
differential invariants. We show that there exist four differential invariants and five semi-invariants
of first order.
Applications of systems that can be transformed by local mappings to simple forms are provided.