Symmetry group classification for general equation

The present paper solves the problem of the group classification of the general equation ut = λu2 x + µuxt where λ and ξ are arbitrary smooth functions of the variable x and u, by using lie method. The paper is one of the few application of an algebraic approach to the problem of group classification. The method of preliminary group classification. A number of new interesting nonlinear invariant models which have nontrivial invariance algebras are obtained the result of the work is a wide class of equations summarized in table form.