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