Kadomtsev-Petviashvili (Kp) nonlinear waves identification

Abstract

By observing the periodic hexagonal pattern of surface waves in a large basin namely the MOB (Manoevering Ocean Basin) various solitons interactions patterns were observed due to the repetition of the interaction patterns of two Kadomtsev- Petviashvili (KP) solitons. This research is a systematic and comprehensive study on the Kadomtsev-Petviashvili (KP) equation. In particular the KP equation is the two dimensional form of the Korteweg-de Vries (KdV) equation. Soliton solutions of the KP equation using Hirota Bilinear method was adopted in this research. Two-soliton solutions of the KP equation can produce a triad, quadruplet and a non-resonance structures. In three-soliton solutions of the KP equation, many other interaction patterns can be observed. For example, a triad with a soliton and a quadruplet with a soliton. A computer program, KPPRO was developed using Microsoft Visual C++ to simulate various interactions patterns.