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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2017, том 13, 053, 14 стр. (Mi sigma1253)

Эта публикация цитируется в 5 статьях

Symmetries of the Hirota Difference Equation

Andrei K. Pogrebkovab

a Steklov Mathematical Institute of Russian Academy of Science, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia

Аннотация: Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented. Commutativity of these symmetries enables interpretation of their parameters as “times” of the nonlinear integrable partial differential-difference and differential equations. Examples of equations resulting in such procedure and their Lax pairs are given. Besides these, ordinary, symmetries the additional ones are introduced and their action on the Scattering data is presented.

Ключевые слова: Hirota difference equation; symmetries; integrable differential-difference and differential equations; additional symmetries.

MSC: 35Q51; 37K10; 37K15; 37K40; 39A14

Поступила: 31 марта 2017 г.; в окончательном варианте 2 июля 2017 г.; опубликована 7 июля 2017 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2017.053



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