Bi-Hamiltonian structure of the Oriented Associativity Equation

Abstract

The Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order non-local homogeneous Hamiltonian operator belonging to a class which has been recently studied, thus providing a highly non-trivial example in that class and showing intriguing connections with algebraic geometry.

15 pages; software is available upon request

References in corpus (4)

• Coisotropic deformations of associative algebras and dispersionless integrable hierarchies
• Systems of conservation laws with third-order Hamiltonian structures
• Computing with Hamiltonian operators
• On a class of third-order nonlocal Hamiltonian operators

Cited by in corpus (5)

• Quasilinear systems of first order PDEs with nonlocal Hamiltonian structures
• WDVV equations and invariant bi-Hamiltonian formalism
• Second-order integrable Lagrangians and WDVV equations
• WDVV equations: Hamiltonian operators and symbolic computations
• Bi-Hamiltonian structures of WDVV-type