SIGMA, 2017, Volume 13, 053, 14 pp.
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
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.
Hirota difference equation; symmetries; integrable differential-difference and differential equations; additional symmetries.
PDF file (378 kB)
MSC: 35Q51; 37K10; 37K15; 37K40; 39A14
Received: March 31, 2017; in final form July 2, 2017; Published online July 7, 2017
Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.
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