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Symmetry, Integrability and Geometry: Methods and Applications, 2017, Volume 13, 057, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2017.057
(Mi sigma1257)
 

This article is cited in 10 scientific papers (total in 10 papers)

On Reductions of the Hirota–Miwa Equation

Andrew N. W. Hone, Theodoros E. Kouloukas, Chloe Ward

School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7NF, UK
References:
Abstract: The Hirota–Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota–Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale–Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.
Keywords: Hirota–Miwa equation; Liouville integrable maps; Somos sequences; cluster algebras.
Funding agency Grant number
Engineering and Physical Sciences Research Council EP/P50421X/1
EP/M004333/1
Some of these results first appeared in the Ph.D. Thesis [28], which was supported by EPSRC studentship EP/P50421X/1. ANWH is supported by EPSRC fellowship EP/M004333/1.
Received: May 2, 2017; in final form July 17, 2017; Published online July 23, 2017
Bibliographic databases:
Document Type: Article
Language: English
Citation: Andrew N. W. Hone, Theodoros E. Kouloukas, Chloe Ward, “On Reductions of the Hirota–Miwa Equation”, SIGMA, 13 (2017), 057, 17 pp.
Citation in format AMSBIB
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
     
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