The single solitary wave with double peaks of the coupled KdV equation and its stability

Abstract

We obtained six classes of exact solutions for the coupled KdV equation by the extended hyperbola function expansion Method.One of the solutions is a solitary wave solution, which has two peaks.This solution is reduced to the kink or bell-like soliton solution of the coupled KdV equation under different limitations. We also investigated the stability of the single solitary wave solution with double peaks numerically.The results indicate that the solution is stable when the amplitude of the disturbance, which has long wave length, and is very small.