Soliton molecules and some related interaction solutions of the (2+1)-dimensional Kadomtsev–Petviashvili hierarchy

Abstract

The [Formula: see text]-soliton solutions of the (2+1)-dimensional Kadomtsev–Petviashvili hierarchy are first constructed. One soliton molecule satisfies the velocity resonance condition, the breather with the periodic solitary wave, the lump soliton localized in all directions in the space are showed successively for [Formula: see text]. Interaction of one soliton molecule and a line soliton, the soliton molecule hybrid a line soliton with the breather/lump soliton are presented for [Formula: see text]. Moreover, the elastic interaction between two-soliton molecules, the interaction between one soliton molecule, and a breather and the elastic collision between the lump soliton and one soliton molecule are also derived for [Formula: see text] by applying the velocity resonance, the module resonance of wave number, and the long-wave limit ideas. Figures are presented to demonstrate these dynamics features.