Symmetries of a class of quasilinear pseudoparabolic equations. Invariant solutions

A qusilinear pseudoparabolic type equation with a free element depending on the second derivative with respect to the spatial variable is researched by the methods of the group analysis. Four-dimensional kernel of principal groups of the equation and specifications of the free element leading to fifth symmetries are found. Optimal systems of one-dimensional subalgebras of the principal Lie algebras for the equations and some invariant solutions are calculated.