Three-Soliton Solutions of The Kadomtsev-Petviashvili Equation

Authors

  • Wei King Tiong
  • Chee Tiong Ong
  • Mukheta Isa

DOI:

https://doi.org/10.11113/matematika.v21.n.509

Abstract

Soliton solutions of the Kadomtsev-Petviashvili (KP) equation which is a two dimensional form of the Korteweg-de Vries (KdV) equation can be obtained by using Hirota Bilinear method. The traditional group-theoretical approach can generate analytic soliton solutions because the KP equation has infinitely many conservation laws. Two-soliton solutions of the KP equation produces a triad, quadruplet and a non-resonant soliton structures in soliton interactions. In three-soliton solutions of the KP equation, we observed two types of interactions patterns namely a triad with a soliton and also a quadruplet with a soliton. Keywords: Soliton; Hirota Bilinear method; Korteweg-de Vries and Kadomtsev-Petviashvili equations Penyelesaian soliton persamaan Kadomtsev-Petviashvili yang merupakan persamaan Korteweg-de Vries (KdV) dua dimensi boleh diperolehi dengan menggunakan kaedah Bilinear Hirota. Kaedah tradisi berasaskan teori kumpulan mampu menjana penyelesaian soliton secara analitik kerana persamaan KP mempunyai ketakterhinggaan banyaknya hukum keabadian. Penyelesaian dua-soliton persamaan KP menghasilkan struktur-struktur berbentuk triad, kuadruplet dan soliton tak beresonan dalam interaksi soliton. Dalam penyelesaian tiga soliton KP, kita dapati dua jenis interaksi iaitu antara triad dengan satu soliton dan antara kuadruplet dengan satu soliton. Katakunci: Soliton; kaedah Bilinear Hirota; persamaan Korteweg-de Vries dan Kadomtsev-Petviashvili.

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Published

01-06-2005

How to Cite

Tiong, W. K., Ong, C. T., & Isa, M. (2005). Three-Soliton Solutions of The Kadomtsev-Petviashvili Equation. MATEMATIKA, 21, 1–13. https://doi.org/10.11113/matematika.v21.n.509

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Section

Mathematics