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.
- Publication:
-
Journal of Physics A Mathematical General
- Pub Date:
- May 2019
- DOI:
- arXiv:
- arXiv:1812.01413
- Bibcode:
- 2019JPhA...52tLT01P
- Keywords:
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- oriented associativity equation;
- associativity equation;
- Hamiltonian formalism;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- 37K05
- E-Print:
- 15 pages