Study on the Integrable Properties of Two Coupled KdV Equations

Abstract

Two coupled KdV equations describing the atmospheric and oceanic phenomena are re-analyzed from the view points of Lie point symmetry, Lie symmetry groups, symmetry reductions, infinitely many generalized symmetries and conservation laws armed with the computer algebra system Maple. The results obtained in this paper show that the two coupled KdV equations are completely integrable in the sense of symmetry and conservation laws. Some results obtained by us are new and first reported here.