Symmetry group classification for general Burgers’ equation

The present paper solves the problem of the group classification of the general Burgers’ equation u t = f ( x , u ) u x 2 + g ( x , u ) u xx , where f and g are arbitrary smooth functions of the variable x and u, by using Lie method. The paper is one of the few applications of an algebraic approach to the problem of group classification that is called preliminary group classification. Looking the adjoint representation of G E on its Lie algebra g 5 , we will deal with the construction of the optimal system of its one-dimensional subalgebras. The result of the work is a wide class of equations summarized in table form.