Kadomtsev–Petviashvili hierarchy: NN-soliton solutions and distinct dispersion relations

In this paper, we investigate the Kadomtsev–Petviashvili (KP) hierarchy that was recently derived. We use the simplified Hirota’s method to study two integrable members of this new KP hierarchy. We show that these two equations give multiple soliton solutions that possess the same amplitude and the same phase shift, but with distinct dispersion relations.