Constructing Initial Value Spaces of Lattice Equations
Exactly Solvable and Integrable Systems
2019-03-28 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
In this paper, we examine the space of initial values for integrable lattice equations, which are lattice equations classified by Adler {\em et al} (2003), known as ABS equations. By considering the map which iterates the solution along particular directions on the lattice, we perform resolutions of singularities for several examples of ABS equations for the first time. Our geometric observations lead to new Miura transformations and reductions to ordinary difference equations.
Cite
@article{arxiv.1807.06162,
title = {Constructing Initial Value Spaces of Lattice Equations},
author = {Nalini Joshi and Sarah Lobb and Matthew Nolan},
journal= {arXiv preprint arXiv:1807.06162},
year = {2019}
}