Twisted reductions of integrable lattice equations, and their Lax representations

Abstract

It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize the periodicity condition by adding a symmetry transformation and apply this idea to autonomous and non-autonomous lattice equations. As results of this approach, we obtain new reductions of the discrete potential Korteweg-de Vries equation, discrete modified Korteweg-de Vries equation and the discrete Schwarzian Korteweg-de Vries equation. We will also describe a direct method for obtaining Lax representations for the reduced equations.

26 pages, 3 figures, 1 table

References in corpus (3)

• An Inverse Scattering Transform for the Lattice Potential KdV Equation
• Reductions of lattice mKdV to $q$-${\mathrm{P}}_{VI}$
• The staircase method: integrals for periodic reductions of integrable lattice equations

Cited by in corpus (3)

• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case
• A Lax pair of a lattice equation whose entropy vanishes