Approximate symmetry reduction to the perturbed coupled KdV equations derived from two-layer fluids

Purpose: The purpose of this paper is to research the solution of the perturbed coupled Korteweg-de Vries (KdV) equations.Methods: The results are obtained through researching a system of corresponding partial differential equations which approximates the perturbed coupled KdV equations and the symmetry method.Results: The symmetry structure and the corresponding general approximate symmetry reduction are derived. Then, using the symmetry reduction, the infinite series solutions are obtained.Conclusions: The approximate symmetry reduction approach can be used to search for similar results of other perturbed nonlinear differential equations with small parameters.