On a discrete analog of the Tzitzeica equation

Abstract

A discrete analog of the Tzitzeica equation is found in the form of quad-equation. Its continuous symmetry is an inhomogeneous Narita--Bogoyavlensky type lattice equation which defines a discretization of the Sawada--Kotera equation. The integrability of these discretizations is proven by construction of the Lax representations.

arXiv comment13 pp

References in corpus (3)

• Recursion operators, conservation laws and integrability conditions for difference equations
• On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
• Classification of integrable discrete Klein-Gordon models

Cited by in corpus (15)

• Darboux transformations and Recursion operators for differential--difference equations
• Classification of five-point differential-difference equations
• On the integrability of a new lattice equation found by multiple scale analysis
• Recursion and Hamiltonian operators for integrable nonabelian difference equations
• Difference systems in bond and face variables and non-potential versions of discrete integrable systems
• Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations
• On reductions of the discrete Kadomtsev--Petviashvili-type equations
• Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations
• On the integrability of a discrete analogue of the Kaup-Kupershmidt equation
• Asymptotic diagonalization of the Discrete Lax pair around singularities and conservation laws for dynamical systems
• ${\mathbb{Z}}_N$ graded discrete Lax pairs and discrete integrable systems
• The structure of rationally factorized Lax type flows and their analytical integrability
• On some new forms of lattice integrable equations
• On the integrability of a lattice equation with two continuum limits
• Recursion operator of the Narita-Itoh-Bogoyavlensky lattice