A project in symmetries of differential equations

Abstract

The aim of the project is to discuss the non-linear wave equations whose coefficients are dependent on first order spatial derivatives. We construct the principal Lie algebra, the equivalence Lie algebra, and the extensions by one of the principal Lie algebra. We further construct the optimal system of one-dimensional sub-algebras for first three extended five dimensional Lie algebras. These are finally used to determine invariant solutions of some examples.