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.
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