On Reductions of the Hirota-Miwa Equation
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On Reductions of the Hirota-Miwa Equation
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| Creator |
Hone, A.N.W.
Kouloukas, T.E. Ward, C. |
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| Description |
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.
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| Date |
2019-02-18T18:48:50Z
2019-02-18T18:48:50Z 2017 |
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| Type |
Article
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| Identifier |
On Reductions of the Hirota-Miwa Equation / A.N.W. Hone, T.E. Kouloukas, C. Ward // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 29 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 70H06; 37K10; 39A20; 39A14; 13F60 DOI:10.3842/SIGMA.2017.057 http://dspace.nbuv.gov.ua/handle/123456789/148768 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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