## ABSTRACT

This chapter shows that the LieOvsiannikov algorithm, which is based on the classical Lie scheme and a set of equivalence transformations (ETs) of the partial differential equations (PDE) class in question, can be applied for solving such kind of problems. The LieOvsiannikov algorithm is based on the classical Lie method and a set of equivalence transformations of the differential equation in question. During the last two decades new approaches for solving the Lie symmetry classification (LSC) problems were developed, which are important for obtaining the so-called canonical list of inequivalent equations admitting nontrivial Lie symmetry algebras. In order to obtain LSC, one needs to construct the principal Lie algebra of the class in question. The technique for constructing the group of equivalence transformations (ETs) is wellknown and is based on a relevant modification of the classical Lie method.