Optimal System and Similarity reductions of a Kind of modi ed Korteweg-de Vries Equation

In this article, we analyze the group variable for modi ed Korteweg-de Vries (mKdV) equation using the Lie group analysise method. It shows that this equation canbe reduced to ODE. We are determined the in nitesimal generators, commutator table of Lie algebra, symmetry group, and similarity reduction for the mKdV equation. Fur-thermore, optimal system, preliminary classi cation of its group invariant solutions and symmetry reduction are examined. Finally this paper shows how to construct directlythe local conservation laws for this equation.