A Review: The Symmetry of the One-Dimensional Burgers Equation

We present the relation between the one-dimensional Burgers equation with the Lie group by applying the prolongation method. The Burgers equation itself is a kind of nonlinear wave equation that generally represents the nonlinear diffusion and can also create both solitary wave solution and multisoliton solution. To use the method, we consider the theorem than can prolong the definition of the partial derivative. The above method produces some generators of its group and by applying the multiplication table it can be shown that the group forms the Lie algebra. We obtain that two generators are the operator of energy and the operator of linear momentum.