A simple-looking relative of the Novikov, Hirota-Satsuma and Sawada-Kotera equations
- 10.1080/14029251.2019.1640465How to use a DOI?
- Integrable equation; Novikov; Hirota-Satsuma; Sawada-Kotera; Bäcklund transformation
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).
- © 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
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 -