Symmetry reduction and some exact solutions of nonlinear biwave equations

Symmetry analysis of a class of biwave equations □2u = F(u) and of a system of wave equations which is equivalent to it is performed. Reduction of the nonlinear biwave equations by means of the Ansätze invariant under non-conjugate subalgebras of the extended Poincaré algebra AP̃(1,1) and the conformal algebra AC(1,1) is carried out. Some exact solutions of these equations are obtained.