Strongly oblique interactions between internal solitary waves with the same mode

In this paper, by using the Lagrangian coordinates, the strongly oblique interactions between solitary waves with the same mode in a stratified fluid are discussed, which includes the shallow fluid case and deep fluid case. It is found that the interactions are described by the KP equation for the shallow fluid case, the two-dimensional intermediate long wave equation (2D-ILW equation) for the deep fluid case and the two-dimensional BO equation (2D-BO equation) for the infinite deep fluid case.