Group analysis of a quasilinear equation

Symmetry analysis is carried out for a second order quasilinear partial differential equation with a free element depending on the phase function. In the nonlinear case two-dimensional principal groups kernel and free element specifications leading to the third symmetries are found. Invariant solutions or submodels are calculated for non-similar one-dimensional subalgebras of the principal Lie algebras with the specifications that were obtained. Conservation laws for the equations are calculated. The linear case with a constant free element is researched also. It is shown that the investigation results don't depend on the equation type.