Two–Soliton Solutions Of The Kadomtsevpetviashvili Equation

Abstract

Beberapa keputusan tentang penjanaan penyelesaian soliton oleh persamaan Kadomtsev–Petviashvili akan dibincangkan dalam kertas ini. Kaedah teori kumpulan mampu memberikan penyelesaian secara analitik kerana persamaan KP mempunyai ketakterhinggaan banyaknya hukum keabadian. Dengan kaedah Bilinear Hirota, ditunjukkan melalui simulasi berkomputer bagaimana penyelesaian dua soliton persamaan KP mampu menghasilkan strukturstruktur “triadâ€, kuadruplet dan struktur tak beresonan dalam interaksi soliton. Kata kunci: Soliton, kaedah Bilinear Hirota, persamaan Kortewegde Vries dan Kadomtsev- Petviashvili Several findings on soliton solutions generated by the Kadomtsev–Petviashvili (KP) equation were discussed in this paper. This equation is a two dimensional of the Korteweg–de Vries (KdV) equation. Traditional group–theoretical approach can generate analytic solution of solitons because KP equation has infinitely many conservation laws. By using Hirota Bilinear method, we show via computer simulation how two solitons solution of KP equation produces triad, quadruplet and a non–resonance structures in soliton interactions. Key words: Soliton, Hirota Bilinear method, Korteweg-de Vries and Kadomtsev-Petviashvili equations