Abstract

On Some Applications of Differential Invariants of a Family of Nonlinear Wave Equations

R.Tracina' (Department of Mathematics and Informatics, University of Catania, Catania, Italy)

e-mail: tracina@dmi.unict.it

We consider a family of nonlinear wave equations studied in (T.T.V.). In that paper we found the equivalence algebra L for these equations and showed that the L is infinite-dimensional. Here, by using an infinitesimal technique developed (NHI) we find differential invariants (see L.V.O.) of this family of differential equations. It is worthwhile noting that the knowledge of invariants of families of equations is essential for the problem of group classification. 1. M. Torrisi, R. Tracina', A. Valenti, On equivalence transformations applied to a non-linear wave equation, Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, Kluwer Academic Publishers, 1993, 367-375. 2. N.H.Ibragimov, Infinitesimal method in the theory of invariants of algebraic and differential equations, Notices of the South African Mathematical Society,29,1997,61-70. 3. L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982.

Section : 12