Hamiltonian Structures for the Ostrovsky-Vakhnenko Equation

TL;DR

This paper develops a bi-Hamiltonian framework for the Ostrovsky-Vakhnenko equation by leveraging its symmetries and a novel transformation, revealing deep structural relations.

Contribution

It introduces a new bi-Hamiltonian formulation for the Ostrovsky-Vakhnenko equation using symmetry and a transformation to a known integrable system.

Findings

Established a bi-Hamiltonian structure for the equation

Linked Hamiltonian structures through variable transformations

Enhanced understanding of the equation's integrability

Abstract

We obtain a bi-Hamiltonian formulation for the Ostrovsky-Vakhnenko equation using its higher order symmetry and a new transformation to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation. Central to this derivation is the relation between Hamiltonian structures when dependent and independent variables are transformed.