On one integrable system with a cubic first integral

TL;DR

This paper analyzes a specific integrable system with a cubic first integral, detailing its bi-Hamiltonian structures and separation variables to deepen understanding of its integrability properties.

Contribution

It introduces the bi-Hamiltonian structures and separation variables for the integrable system studied by Valent, providing new insights into its mathematical framework.

Findings

Identification of bi-Hamiltonian structures

Derivation of variables of separation

Enhanced understanding of the system's integrability

Abstract

Recently one integrable model with a cubic first integral of motion has been studied by Valent using some special coordinate system. We describe the bi-Hamiltonian structures and variables of separation for this system.