Bi-Hamiltonian structure of the oriented associativity equation

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...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2019-05, Vol.52 (20), p.20
Main Authors: Pavlov, Maxim V, Vitolo, Raffaele F
Format: Article
Language:English
Subjects:
associativity equation
Hamiltonian formalism
oriented associativity equation
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Summary: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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab15f4