On a discrete analog of the Tzitzeica equation
V.E. Adler
TL;DR
This paper introduces a discrete version of the Tzitzeica equation as a quad-equation, demonstrating its integrability through Lax representations and connecting it to a discretized Sawada--Kotera equation.
Contribution
It presents a novel discrete analog of the Tzitzeica equation and establishes its integrability via Lax pairs, linking it to a discretized Sawada--Kotera equation.
Findings
Discrete Tzitzeica analog formulated as a quad-equation
Integrability proven through Lax representations
Connects to a discretized Sawada--Kotera 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Quantum chaos and dynamical systems