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Эта публикация цитируется в 10 научных статьях (всего в 10 статьях)
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
Аннотация:
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.
Ключевые слова:
Hirota–Miwa equation; Liouville integrable maps; Somos sequences; cluster algebras.
Поступила: 2 мая 2017 г.; в окончательном варианте 17 июля 2017 г.; опубликована 23 июля 2017 г.
Образец цитирования:
Andrew N. W. Hone, Theodoros E. Kouloukas, Chloe Ward, “On Reductions of the Hirota–Miwa Equation”, SIGMA, 13 (2017), 057, 17 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1257 https://www.mathnet.ru/rus/sigma/v13/p57
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