Lie Group Analysis of a Nonlinear Coupled System of Korteweg-de Vries Equations

Abstract

In this paper, we consider coupled Korteweg-de 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. The method of Lie group analysis is used to on the system to obtain symmetry reductions. Soliton solutions are constructed by use of a linear combination of time and space translation symmetries. Furthermore, we compute conservation laws in two ways that is by multiplier method and by an application of new conservation theorem developed by Nail Ibragimov.

Keywords

• coupled kdv equations
• lie group analysis
• group-invariant solutions
• stationary solutions
• symmetry reductions
• soliton
• multipliers
• conservation laws