Journal of Nonlinear Mathematical Physics

Volume 16, Issue 2, June 2009, Pages 179 - 194

Solutions of the (2 + 1)-Dimensional KP, SK and KK Equations Generated by Gauge Transformations from Nonzero Seeds

Authors
Jingsong He*, Xiaodong Li
Department of Mathematics, University of Science and Technology of China, Hefei, 230026 Anhui, P. R. China
Received 6 October 2008, Accepted 25 November 2008, Available Online 7 January 2021.
DOI
10.1142/S1402925109000170How to use a DOI?
Keywords
Gauge transformation; soliton; KP equation; BKP equation; CKP equation
Abstract

By using gauge transformations, we manage to obtain new solutions of (2 + 1)-dimensional Kadomtsev–Petviashvili (KP), Kaup–Kuperschmidt (KK) and Sawada–Kotera (SK) equations from nonzero seeds. For each of the preceding equations, a Galilean type transformation between these solutions u2 and the previously known solutions u2 generated from zero seed is given. We present several explicit formulas of the single-soliton solutions for u2 and u2, and further point out the two main differences of them under the same value of parameters, i.e., height and location of peak line, which are demonstrated visibly in three figures.

Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - 2
Pages
179 - 194
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925109000170How to use a DOI?
Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Jingsong He
AU  - Xiaodong Li
PY  - 2021
DA  - 2021/01/07
TI  - Solutions of the (2 + 1)-Dimensional KP, SK and KK Equations Generated by Gauge Transformations from Nonzero Seeds
JO  - Journal of Nonlinear Mathematical Physics
SP  - 179
EP  - 194
VL  - 16
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000170
DO  - 10.1142/S1402925109000170
ID  - He2021
ER  -