Hamiltonian Structures for the Ostrovsky-Vakhnenko Equation

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.

13 pages

References in corpus (5)

• The short pulse equation is integrable
• A New Integrable Equation with Peakon Solutions
• Integrable and non-integrable equations with peakons
• Wave breaking in the Ostrovsky--Hunter equation
• On integrability of one third-order nonlinear evolution equation

Cited by in corpus (11)

• Transformation and integrability of a generalized short pulse equation
• Integrable semi-discretizations of the reduced Ostrovsky equation
• A convergent finite difference scheme for the Ostrovsky--Hunter equation with Dirichlet boundary conditions
• The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited
• Integrability of a generalized short pulse equation revisited
• Reciprocal link for a coupled Camassa-Holm type equation
• A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue
• On Spatial Discretization of Evolutionary Differential Equations on the Periodic Domain with a Mixed Derivative
• Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation
• On a new avatar of the sine-Gordon equation
• On The Complete Integrability Of The Ostrovsky-Vakhnenko Equation