Using the basic Lie symmetry method, we find the most general Lie point symmetries group of the inviscid Burgers’ equation.
Looking at the adjoint representation of the obtained symmetry group on its Lie algebra, we find the preliminary classification
of its group-invariant solutions. The latter provides new exact solutions for the inviscid Burgers’ equation.
Mathematics Subject Classification (2000). 70G65 - 58K70 - 34C14
Keywords. Lie-point symmetries - similarity solution - optimal system of Lie sub-algebras
Received: July 10, 2008. Accepted: August 29, 2008.