Modeling rogue waves with the Kadomtsev-Petviashvili (KP) equation (Q1799904)

The aim of this paper is to derive a new class of solutions for the Kadomtsev-Petviashvili (KP) equation, and to discuss their possible relevance to rogue waves (also called giant or freak waves). The nonlinear interaction of these solutions is considered. The authors used the KP equation to show the basic mechanism of rogue waves. Through many simulations on their interactions, the solutions obtained repeatedly showed the appearance of large-amplitude waves with a short life span that appear seemingly from nowhere and may cause great destruction. The solutions obtained in this paper are from the dimensionless form of the KP equation. As a result, contributions from physical parameters like wind, gravity, density and surface tension were lost. This paper is organized as follows: Section 1 contains background and motivation. Section 2 is devoted to intuitive derivation of the KP equations: A mathematical approach. Section 3 contains the main results and Section 4 is devoted to singular solutions. Section 5 deals with interaction of singular solutions. Section 6 is devoted to conclusions. Finally, some proofs are given in Section 7.