Darboux transformations with tetrahedral reduction group and nonlocal symmetries
Date/Time: 10:50 07-Aug-2014
We study Lax-Darboux scheme which is invariant with respect to the tetrahedral
reduction group. We have found a generic and four degenerate elementary Darboux
maps and corresponding differential-difference (D$\Delta $Es) and
partial-deference (P$\Delta $Es) integrable systems.
Some of these P$\Delta$Es have a reduction to a scalar 6-point equation, which
can be regarded as a difference analogue of Kuprschmidt's KdV6 equation.
Differential-difference equations are non-local symmetries of the corresponding
partial-difference systems. We are making steps towards the extension of the
Symmetry approach to the case of non-local symmetries.
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