Novel methods for finding general forms of new multi-soliton solutions to (1+1)-dimensional KdV equation and (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation

Chun Ku Kuo, Sen-Yung Lee

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, two novel methods used to solve (1+1) and (2+1)-dimensional completely integrable equations are proposed. The methods are applied to handle the KdV and Kadomtsev–Petviashvili (KP) equations with variable coefficients, and the general forms of new multi-soliton solutions are formally obtained, respectively. In addition, the new multi-soliton solution is suitable to two different type KP equations. Comparing with the Hirota’s method, the results show that new methods are straightforward handling the KdV and KP equations without conjecturing the transformation and good in dealing the equations with variable coefficients.

Original languageEnglish
Pages (from-to)569-579
Number of pages11
JournalWaves in Random and Complex Media
Volume29
Issue number3
DOIs
Publication statusPublished - 2019 Jul 3

Fingerprint

Solitons
solitary waves
coefficients

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

@article{7a82cfed0f3b4b3abe16a9f751df9cf0,
title = "Novel methods for finding general forms of new multi-soliton solutions to (1+1)-dimensional KdV equation and (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation",
abstract = "In this paper, two novel methods used to solve (1+1) and (2+1)-dimensional completely integrable equations are proposed. The methods are applied to handle the KdV and Kadomtsev–Petviashvili (KP) equations with variable coefficients, and the general forms of new multi-soliton solutions are formally obtained, respectively. In addition, the new multi-soliton solution is suitable to two different type KP equations. Comparing with the Hirota’s method, the results show that new methods are straightforward handling the KdV and KP equations without conjecturing the transformation and good in dealing the equations with variable coefficients.",
author = "Kuo, {Chun Ku} and Sen-Yung Lee",
year = "2019",
month = "7",
day = "3",
doi = "10.1080/17455030.2018.1456703",
language = "English",
volume = "29",
pages = "569--579",
journal = "Waves in Random and Complex Media",
issn = "1745-5030",
publisher = "Taylor and Francis Ltd.",
number = "3",

}

TY - JOUR

T1 - Novel methods for finding general forms of new multi-soliton solutions to (1+1)-dimensional KdV equation and (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation

AU - Kuo, Chun Ku

AU - Lee, Sen-Yung

PY - 2019/7/3

Y1 - 2019/7/3

N2 - In this paper, two novel methods used to solve (1+1) and (2+1)-dimensional completely integrable equations are proposed. The methods are applied to handle the KdV and Kadomtsev–Petviashvili (KP) equations with variable coefficients, and the general forms of new multi-soliton solutions are formally obtained, respectively. In addition, the new multi-soliton solution is suitable to two different type KP equations. Comparing with the Hirota’s method, the results show that new methods are straightforward handling the KdV and KP equations without conjecturing the transformation and good in dealing the equations with variable coefficients.

AB - In this paper, two novel methods used to solve (1+1) and (2+1)-dimensional completely integrable equations are proposed. The methods are applied to handle the KdV and Kadomtsev–Petviashvili (KP) equations with variable coefficients, and the general forms of new multi-soliton solutions are formally obtained, respectively. In addition, the new multi-soliton solution is suitable to two different type KP equations. Comparing with the Hirota’s method, the results show that new methods are straightforward handling the KdV and KP equations without conjecturing the transformation and good in dealing the equations with variable coefficients.

UR - http://www.scopus.com/inward/record.url?scp=85045035847&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045035847&partnerID=8YFLogxK

U2 - 10.1080/17455030.2018.1456703

DO - 10.1080/17455030.2018.1456703

M3 - Article

AN - SCOPUS:85045035847

VL - 29

SP - 569

EP - 579

JO - Waves in Random and Complex Media

JF - Waves in Random and Complex Media

SN - 1745-5030

IS - 3

ER -