Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 3, May 2020, Pages 393 - 413

Integrable Boundary Conditions for the Hirota-Miwa Equation and Lie Algebras

Authors
Ismagil Habibullin
Department of Mathematical Physics, Institute of Mathematics Ufa Federal Research Centre, Russian Academy of Sciences 112, Chernyshevsky Street, Ufa 450008, Russian Federation Bashkir State University, 32 Validy Street, Ufa 450076, Russian Federation,habibullinismagil@gmail.com
Aigul Khakimova
Department of Mathematical Physics, Institute of Mathematics Ufa Federal Research Centre, Russian Academy of Sciences 112, Chernyshevsky Street, Ufa 450008, Russian Federation,aigul.khakimova@mail.ru
Received 14 June 2019, Accepted 13 October 2019, Available Online 4 May 2020.
DOI
10.1080/14029251.2020.1757229How to use a DOI?
Keywords
Discretization; integrability; quad equations
Abstract

Systems of discrete equations on a quadrilateral graph related to the series DN(2) of the affine Lie algebras are studied. The systems are derived from the Hirota-Miwa equation by imposing boundary conditions compatible with the integrability property. The Lax pairs for the systems are presented. It is shown that in the continuum limit the quad systems tend to the corresponding systems of the differential equations belonging to the well-know Drinfeld-Sokolov hierarchies. The problem of finding the formal asymptotic expansion of the solutions to the Lax equations is studied. Generating functions for the local conservation laws are found for the system corresponding to D3(2). An example of the higher symmetry is presented.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 3
Pages
393 - 413
Publication Date
2020/05/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1757229How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Ismagil Habibullin
AU  - Aigul Khakimova
PY  - 2020
DA  - 2020/05/04
TI  - Integrable Boundary Conditions for the Hirota-Miwa Equation and Lie Algebras
JO  - Journal of Nonlinear Mathematical Physics
SP  - 393
EP  - 413
VL  - 27
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1757229
DO  - 10.1080/14029251.2020.1757229
ID  - Habibullin2020
ER  -