SIGMA 6 (2010), 092, 14 pages      arXiv:1010.0361     https://doi.org/10.3842/SIGMA.2010.092

On Non-Point Invertible Transformations of Difference and Differential-Difference Equations

Sergey Ya. Startsev
Ufa Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky Str., Ufa, 450077, Russia

Received October 04, 2010, in final form December 03, 2010; Published online December 11, 2010

Abstract
Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are used to construct new examples of integrable equations and autotransformations of the Hietarinta equation.

Key words: non-point transformation; Darboux integrability; discrete Liouville equation; higher symmetry.

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