Hamiltonian structures for the Ostrovsky–Vakhnenko equation

We obtain a bi-Hamiltonian formulation for the Ostrovsky–Vakhnenko (OV) 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.

► A fifth order Ostrovsky–Vakhnenko equation is shown to be related with the Caudrey–Dodd–Gibbon–Sawada–Kotera equation.
► The bi-Hamiltonian formulation for Ostrovsky–Vakhnenko equation is derived.
► The relation between Hamiltonian structures when dependent and independent variables are transformed is studied.