Exact symmetry reduction solutions of a nonlinear coupled system of Korteweg-De Vries Equations

We study a system of coupled Kortewegde Vries equations that model the propagation of shallow water waves, ion- acoustic waves in plasmas, solitons, and nonlinear perturbations along internal surfaces between layers of different densities in stratified fluids, for example propagation of solitons of long internal waves in oceans. Other applications of this kind of equations have been to model shock wave formation, turbulence, boundary layer behavior, and mass transport. The method presented is Lie group analysis. We first obtain Lie point symmetries and use them to carry out symmetry reductions and the resulting systems investigated for solutions. Traveling waves are constructed by use of a linear combination of time and space translation symmetries.