RUS  ENG
Полная версия
ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2017, том 13, 057, 17 стр. (Mi sigma1257)

Эта публикация цитируется 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.

MSC: 70H06; 37K10; 39A20; 39A14; 13F60

Поступила: 2 мая 2017 г.; в окончательном варианте 17 июля 2017 г.; опубликована 23 июля 2017 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2017.057



Реферативные базы данных:


© МИАН, 2024