Symmetry analysis of nonlinear pseudoparabolic equation

The group classification is obtained for quasilinear pseudoparabolic equation with a free element depending on the first order time derivative. Four-dimensional kernel of principal groups and all free element specifications up to equivalence transformations which correspond to additional symmetries of the equation are found. For some nonlinear specifications optimal one-dimensional subalgebras system of five-dimensional principal Lie algebra and corresponding invariant solutions or invariant submodels are calculated. Besides, nonlinear self-adjointness is shown for the operator that defining the linear equation of the species. A series of conservation laws of a linear equation was searched.