Abstract

In this paper, classical and nonclassical symmetries of the potential KdV equation are considered. A catalogue of symmetry reductions for potential KdV equation is obtained using the classical Lie method and nonclassical method due to Bluman and Cole.^[1] The Lie algebra consists of five finite parameter Lie group transformations; two being the scaling symmetry and the others being translations. By using the nonclassical method, four finite parameter group transformations are obtained. Two different types of solutions, approximate and exact solutions, are found by using the symmetries. Using the classical symmetries, only approximate series solutions are constructed, but using the nonclassical symmetries, both the exact solution and the approximate solution were found. The advantage of nonclassical symmetries is that the exact solution of the KdV equation can be found with it. Perturbation method is also used for approximate solutions.