# New bi-Hamiltonian systems on the plane

## TL;DR

This paper introduces new bi-Hamiltonian integrable systems on the plane, detailing their integrals of motion, separation variables, and compatible Poisson structures using the Jacobi method.

## Contribution

It presents novel bi-Hamiltonian systems with higher-order integrals of motion and explicit separation variables, expanding the class of known integrable systems.

## Key findings

- New bi-Hamiltonian systems with third, fourth, and sixth order integrals
- Explicit separated relations and variables provided
- Compatible Poisson brackets and recursion operators constructed

## Abstract

We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth and sixth order in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets and recursion operators are also presented in the framework of the Jacobi method.