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

[摘要] 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.

[关键词] non-point transformation;Darboux integrability;discrete Liouville equation;higher symmetry