On Reductions of the Hirota-Miwa Equation
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 equatio...
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| Дата: | 2017 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148768 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1487682019-02-19T01:31:19Z On Reductions of the Hirota-Miwa Equation Hone, A.N.W. Kouloukas, T.E. Ward, C. 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. 2017 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Hone, A.N.W. Kouloukas, T.E. Ward, C. |
| spellingShingle |
Hone, A.N.W. Kouloukas, T.E. Ward, C. On Reductions of the Hirota-Miwa Equation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Hone, A.N.W. Kouloukas, T.E. Ward, C. |
| author_sort |
Hone, A.N.W. |
| title |
On Reductions of the Hirota-Miwa Equation |
| title_short |
On Reductions of the Hirota-Miwa Equation |
| title_full |
On Reductions of the Hirota-Miwa Equation |
| title_fullStr |
On Reductions of the Hirota-Miwa Equation |
| title_full_unstemmed |
On Reductions of the Hirota-Miwa Equation |
| title_sort |
on reductions of the hirota-miwa equation |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148768 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:31:04Z |
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2023-05-20T17:31:04Z |
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