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This article is cited in 5 scientific papers (total in 5 papers)
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
Abstract:
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.
Keywords:
Hirota difference equation; symmetries; integrable differential-difference and differential equations; additional symmetries.
Received: March 31, 2017; in final form July 2, 2017; Published online July 7, 2017
Citation:
Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1253 https://www.mathnet.ru/eng/sigma/v13/p53
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Abstract page: | 1794 | Full-text PDF : | 34 | References: | 28 |
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