Microscopic conservation laws for integrable lattice models
Analysis of PDEs
2020-12-10 v1 Exactly Solvable and Integrable Systems
Abstract
We consider two discrete completely integrable evolutions: the Toda Lattice and the Ablowitz-Ladik system. The principal thrust of the paper is the development of microscopic conservation laws that witness the conservation of the perturbation determinant under these dynamics. In this way, we obtain discrete analogues of objects that we found essential in our recent analyses of KdV, NLS, and mKdV. In concert with this, we revisit the classical topic of microscopic conservation laws attendant to the (renormalized) trace of the Green's function.
Cite
@article{arxiv.2012.04782,
title = {Microscopic conservation laws for integrable lattice models},
author = {Benjamin Harrop-Griffiths and Rowan Killip and Monica Visan},
journal= {arXiv preprint arXiv:2012.04782},
year = {2020}
}
Comments
22 pages