Examples of Darboux Integrable Discrete Equations Possessing First Integrals of an Arbitrarily High Minimal Order

Abstract

We consider a discrete equation, defined on the two-dimensional square lattice, which is linearizable, namely, of the Burgers type and depends on a parameter $\alpha$. For any natural number $N$ we choose $\alpha$ so that the equation becomes Darboux integrable and the minimal orders of its first integrals in both directions are greater or equal than $N$.

7 pages, submitted to Ufa Mathematical Journal

References in corpus (2)

• Discrete analogues of the Liouville equation
• A new two-dimensional lattice model that is "consistent around a cube"

Cited by in corpus (5)

• Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations
• An unusual series of autonomous discrete integrable equations on the square lattice
• On Darboux non-integrability of the Hietarinta equation
• Modified series of integrable discrete equations on a square lattice with a non-standard symmetry structure
• On a series of Darboux integrable discrete equations on the square lattice