I. Introduction
AN INTERNAL solitary wave is a localized internal gravity wave that occurs in a stratified fluid. It induces strong vertical motion, vertical shear of horizontal velocity, density perturbations, and probably nutrient pumping [1]. It also impacts the stability of oil platforms [2], the security of submarine navigation [3], and underwater acoustic propagation [4]–[7]. In 1834, Russell [8], [9] made the first observation of solitary waves. Boussinseq [10] and Korteweg and deVries [11] gave a theoretical description, hereafter referred to as KdV, which represented the extent of physical understanding of solitary waves up to that time. The solitary wave has a particle-like behavior. Zabusky and Kruskal [12] coined the word “soliton” to describe it.