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Discrete Hirota reductions associated with the lattice KdV equation

Hone, Andrew N.W., Kouloukas, Theodoros E. (2020) Discrete Hirota reductions associated with the lattice KdV equation. Journal of Physics A: Mathematical and Theoretical, . Article Number UNSPECIFIED. ISSN 1751-8113. (In press) (doi:10.1088/1751-8121/aba1b8) (KAR id:81455)

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http://dx.doi.org/10.1088/1751-8121/aba1b8

Abstract

We study the integrability of a family of birational maps obtained as reductions of the discrete Hirota equation, which are related to travelling wave solutions of the lattice KdV equation. In particular, for reductions corresponding to waves moving with rational speed N/M on the lattice, where N,M are coprime integers, we prove the Liouville integrability of the maps when N + M is odd, and prove various properties of the general case. There are two main ingredients to our construction: the cluster algebra associated with each of the Hirota bilinear equations, which provides invariant (pre)symplectic and Poisson structures; and the connection of the monodromy matrices of the dressing chain with those of the KdV travelling wave reductions.

Item Type: Article
DOI/Identification number: 10.1088/1751-8121/aba1b8
Uncontrolled keywords: Hirota equations; Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Theodoros Kouloukas
Date Deposited: 30 May 2020 00:25 UTC
Last Modified: 28 Jul 2020 11:24 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/81455 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
Kouloukas, Theodoros E.: https://orcid.org/0000-0002-9903-6788
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