The Schwarzian variable associated with discrete KdV-type equations
Exactly Solvable and Integrable Systems
2010-10-12 v1
Abstract
We present a new construction related to systems of polynomials which are consistent on a cube. The consistent polynomials underlie the integrability of discrete counterparts of integrable partial differential equations of Korteweg- de Vries-type (KdV-type). The construction reported here associates a Schwarzian variable to such systems. In the generic case, including the primary model Q4, the new variable satisfies the lattice Schwarzian Kadomtsev-Petviashvili (KP) equat ion in three dimensions. For the degenerate sub-cases of Q4 the same construction reveals an invertible transformation to the lattice Schwarzian KdV equation.
Cite
@article{arxiv.1010.1916,
title = {The Schwarzian variable associated with discrete KdV-type equations},
author = {James Atkinson and Nalini Joshi},
journal= {arXiv preprint arXiv:1010.1916},
year = {2010}
}
Comments
17 pages