Journal of Nonlinear Mathematical Physics

Volume 16, Issue 2, June 2009, Pages 127 - 139

Solutions of the Extended Kadomtsev–Petviashvili–Boussinesq Equation by the Hirota Direct Method

Authors
Asli Pekcan
Department of Mathematics, Faculty of Science, Bilkent University, 06800 Ankara, Turkey
Received 29 January 2007, Accepted 29 August 2008, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925109000121How to use a DOI?
Keywords
The Hirota direct method, non-integrable equations, exact solutions, solitons, Kadomtsev–Petviashvili equation, Boussinesq equation
Abstract

We show that we can apply the Hirota direct method to some non-integrable equations. For this purpose, we consider the extended Kadomtsev–Petviashvili–Boussinesq (eKPBo) equation with M variable which is

(uxxx6uux)x+a11uxx+2k=2Ma1kuxxk+i,j=2Maijuxixj=0,
where aij = aji are constants and xi = (x, t, y, z, . . . ,xM). We will give the results for M = 3 and a detailed work on this equation for M = 4. Then we will generalize the results for any integer M > 4.

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
127 - 139
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925109000121How 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  - Asli Pekcan
PY  - 2021
DA  - 2021/01
TI  - Solutions of the Extended Kadomtsev–Petviashvili–Boussinesq Equation by the Hirota Direct Method
JO  - Journal of Nonlinear Mathematical Physics
SP  - 127
EP  - 139
VL  - 16
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000121
DO  - https://doi.org/10.1142/S1402925109000121
ID  - Pekcan2021
ER  -