Author(s) : F. D. KamanoPages : [1] - [19]
Received : October 21, 2015; Revised November 25, 2015
Communicated by : Professor Emrullah Yasar
This paper focuses on the symmetries of the Gardner equation or the combined Korteweg-de Vries-modified Korteweg-de Vries (KdV-mKdV) equation. The differential form technique, which is called Harrison method for finding the point symmetry algebra will be explained for the Gardner equation. This will be treated in Section 2, obtaining three dimensional Lie point transformations for the equation. The results obtained from the Harrison approach have been tested and confirmed with the Lie method, in Section 3. Finally, a generalized form of solutions to the Gardner equation is exhibited in Section 4, using the symmetry group of the equation.
symmetries, differential forms, Korteweg-de Vries equations.
