Eur. Phys. J. Plus (2022) 137: 337
https://doi.org/10.1140/epjp/s13360-022-02554-5

Regular Article

A scalar fourth-order integrable equation associated with $\text{so}(3,\mathbb{R})$

¹ College of Mathematics and Compute Science, Quanzhou Normal University, 362000, Quanzhou, Fujian, China
² Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, Zhejiang, China
³ Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
⁴ Department of Mathematics and Statistics, University of South Florida, 33620-5700, Tampa, FL, USA
⁵ School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, 2735, Mmabatho, South Africa

^b mawx@cas.usf.edu

Received: 18 June 2021
Accepted: 3 March 2022
Published online: 13 March 2022

Abstract

We construct a scalar fourth-order integrable equation reduced from an integrable system associated with the special orthogonal Lie algebra $\text{so}(3,\mathbb{R})$. The resulting reduced fourth-order integrable equation inherits a bi-Hamiltonian structure, which leads to infinitely many commuting symmetries and conservation laws.