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

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.

References in corpus (5)

• Discrete analogues of the Liouville equation
• Recursion operators, conservation laws and integrability conditions for difference equations
• A new two-dimensional lattice model that is "consistent around a cube"
• The Generalized Symmetry Method for Discrete Equations
• Characteristic Algebras of Fully Discrete Hyperbolic Type Equations

Cited by in corpus (8)

• Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf-Cole Transformations
• Non-Point Invertible Transformations and Integrability of Partial Difference Equations
• Darboux integrable discrete equations possessing an autonomous first-order integral
• Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation
• Modified series of integrable discrete equations on a square lattice with a non-standard symmetry structure
• On Darboux non-integrability of the Hietarinta equation
• On a series of Darboux integrable discrete equations on the square lattice
• Classification of semidiscrete hyperbolic type equations. The case of fifth order symmetries