Journal of Nonlinear Mathematical Physics

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Volume 26, Issue 4, July 2019, Pages 555 - 568

A simple-looking relative of the Novikov, Hirota-Satsuma and Sawada-Kotera equations

Authors
Alexander G. Rasin
Department of Mathematics, Ariel University, Ariel 40700, Israel,rasin@ariel.ac.il
Jeremy Schiff
Department of Mathematics, Bar-Ilan University, Ramat Gan, 52900, Israel,schiff@math.biu.ac.il
Received 9 April 2019, Accepted 4 May 2019, Available Online 9 July 2019.
DOI
10.1080/14029251.2019.1640465How to use a DOI?
Keywords
Integrable equation; Novikov; Hirota-Satsuma; Sawada-Kotera; Bäcklund transformation
Abstract

We study the simple-looking scalar integrable equation fxxt − 3(fx ft − 1) = 0, which is related (in different ways) to the Novikov, Hirota-Satsuma and Sawada-Kotera equations. For this equation we present a Lax pair, a Bäcklund transformation, soliton and merging soliton solutions (some exhibiting instabilities), two infinite hierarchies of conservation laws, an infinite hierarchy of continuous symmetries, a Painlevé series, a scaling reduction to a third order ODE and its Painlevé series, and the Hirota form (giving further multisoliton solutions).

Copyright
© 2019 The Authors. Published by Atlantis 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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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
26 - 4
Pages
555 - 568
Publication Date
2019/07/09
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2019.1640465How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis 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

risenwbib
TY  - JOUR
AU  - Alexander G. Rasin
AU  - Jeremy Schiff
PY  - 2019
DA  - 2019/07/09
TI  - A simple-looking relative of the Novikov, Hirota-Satsuma and Sawada-Kotera equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 555
EP  - 568
VL  - 26
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1640465
DO  - 10.1080/14029251.2019.1640465
ID  - Rasin2019
ER  -