Optimal System, Lie Symmetries Group Analysis and Similarity reductions of the Nonlinear Di usion Boussinesq Equation

In this paper, we obtain the Lie symmetry group of the di usion Boussinesq equation. Lie symmetry group helps us to obtain new solutions from known one. Thenwe analysis this group and classify the one dimensional subalgebra of the Lie symmetry algebra of the di usion Boussinesq equation. we have found optimal system and pre-liminary classi cation of group-invariant solution and we construct the optimal system of one-dimensional subalgebras for the Lie symmetry algebra of this equation. Further-more, similarity reductions related to the in nitesimal generators of the Lie symmetry group are obtained.

Keywords:

Boussinesq Equation , Optimal System , Lie Symmetry , Similarity Reduc- tion.