On the open Toda chain with external forcing
Dynamical Systems
2020-12-07 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We consider the open Toda chain with external forcing, and in the case when the forcing stretches the system, we derive the longtime behavior of solutions of the chain. Using an observation of J\"{u}rgen Moser, we then show that the system is completely integrable, in the sense that the -dimensional system has functionally independent Poisson commuting integrals, and also has a Lax-Pair formulation. In addition, we construct action-angle variables for the flow. In the case when the forcing compresses the system, the analysis of the flow remains open.
Keywords
Cite
@article{arxiv.2012.02244,
title = {On the open Toda chain with external forcing},
author = {Percy Deift and Luen-Chau Li and Herbert Spohn and Carlos Tomei and Thomas Trogdon},
journal= {arXiv preprint arXiv:2012.02244},
year = {2020}
}