Multi soliton solution for the system of Coupled Korteweg-de Vries equations

In this paper we consider the system of coupled Korteweg-de Vries equations and establish the transformation which turns the coupled KdV equations into the single nonlinear partial differential equation, then we obtain an auto-Bäcklund transformation and Lax pairs by using the extended homogeneous balance method. Also, we obtain the multi soliton solutions and the new trigonometric function periodic solutions by using the generalized tanh method.