Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivska Street, 01601 Kyiv-4, UKRAINE
e-mail: magda@imath.kiev.ua

Invariance of the quasilinear equations of hyperbolic type with respect to the three-parametric Lie algebras.

Abstract:
We have completely solved the problem of group classification of quasi-linear hyperbolic differential equations in two independent variables that are invariant under one-, two- and three-parameter Lie groups. What is more, we describe all equations of the considered form that admit four-parameter split solvable Lie groups.