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Recursion and Hamiltonian Operators for Integrable Nonabelian Difference Equations

Casati, Matteo, Wang, Jing Ping (2020) Recursion and Hamiltonian Operators for Integrable Nonabelian Difference Equations. Nonlinearity, 34 (1). Article Number 205. ISSN 0951-7715. (doi:10.1088/1361-6544/aba88c) (KAR id:82506)

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https://doi.org/10.1088/1361-6544/aba88c

Abstract

In this paper, we carry out the algebraic study of integrable differential-difference equations whose field variables take values in an associative (but not commutative) algebra. We adapt the Hamiltonian formalism to nonabelian difference Laurent polynomials and describe how to obtain a recursion operator from the Lax representation of an integrable nonabelian differential-difference system. As an application, we propose a novel family of integrable equations: the nonabelian NaritaItoh-Bogoyavlensky lattice, for which we construct their recursion operators and Hamiltonian operators and prove the locality of infinitely many commuting symmetries generated from their highly nonlocal recursion operators. Finally, we discuss the nonabelian version of several

integrable difference systems, including the relativistic Toda chain and Ablowitz-Ladik lattice.

Item Type: Article
DOI/Identification number: 10.1088/1361-6544/aba88c
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Jing Ping Wang
Date Deposited: 18 Aug 2020 15:15 UTC
Last Modified: 09 Nov 2021 00:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/82506 (The current URI for this page, for reference purposes)
Casati, Matteo: https://orcid.org/0000-0002-2207-4807
Wang, Jing Ping: https://orcid.org/0000-0002-6874-5629
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