Genus-Two Solutions to the Kadomtsev — Petviashvili Equation

Abstract

In this paper we consider dynamical aspects of multi-directional waves described by the Kadomtsev-Petviashvili (KP) equation. We investigate some analytically known solutions: the two-soliton interacting waves and their periodic equivalents. It is shown that the behaviour of the interaction of two-solitons can be classified by a parameter A ≥ 0 (depending on the amplitudes of pure one-solitons and the angles of interactions). In the limiting case when A = 0, it is found that the two-soliton reduces to a three-branch soliton.