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.

13 pp

References in corpus (1)

• On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations

Cited by in corpus (6)

• Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations
• Asymptotic diagonalization of the Discrete Lax pair around singularities and conservation laws for dynamical systems
• On the integrability of a discrete analogue of the Kaup-Kupershmidt equation
• ${\mathbb{Z}}_N$ graded discrete Lax pairs and discrete integrable systems
• The structure of rationally factorized Lax type flows and their analytical integrability
• On the integrability of a lattice equation with two continuum limits