Abstract

Differential Invariants for a Class of Nonlinear Wave Equations

M.Torrisi, A.Valenti (Dipartimento di Matematica e Informatica, University of Catania, Catania, Italy); N.H.Ibragimov (Research Centre ALGA: Advances in Lie Group Analysis, Department of Health, Science and Mathematics, Blekinge Institute of Technology, Karlskrona, Sweden)

e-mail: torrisi@dmi.unict.it

We consider a class of wave equations studied some ten years and by applying an infinitesimal technique recently developed by one of the A.A. (NHI) that allows to find invariants of families of differential equations possessing finite or infinite equivalence groups. It is worth noting that the method does not depend on the assumption of linearity of equations. Here, we apply this method for calculation of invariants for the class of nonlinear equations under consideration. We show that the infinite-dimensional equivalence Lie algebra has three functionally independent differential invariants of the second order. Knowledge of invariants of families of equations is essential for identifying distinctly different equations and therefore for the problem of group classification.

Section : 12