Nijhoff, F, Sun, Y and Zhang, D (Cover date: April 2023) Elliptic Solutions of Boussinesq Type Lattice Equations and the Elliptic Nth Root of Unity. Communications in Mathematical Physics, 399. pp. 599-650. ISSN 0010-3616
Abstract
We establish an infinite family of solutions in terms of elliptic functions of the lattice Boussinesq systems by setting up a direct linearisation scheme, which provides the solution structure for those equations in the elliptic case. The latter, which contains as main structural element a Cauchy kernel on the torus, is obtained from a dimensional reduction of the elliptic direct linearisation scheme of the lattice Kadomtsev–Petviashvili equation, which requires the introduction of a novel technical concept, namely the ‘elliptic cube root of unity’. Thus, in order to implement the reduction we define, more generally, the notion of elliptic Nth root of unity, and discuss some of its properties in connection with a special class of elliptic addition formulae. As a particular concrete application we present the class of elliptic multi-soliton solutions of the lattice Boussinesq systems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Crown 2022. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Dec 2022 15:37 |
Last Modified: | 30 Aug 2023 15:00 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00220-022-04567-8 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:193674 |