On the open Toda chain with external forcing

2020/12/03 by Percy Deift, Deift, Percy, Luen-Chau Li +7 · 1 citation
Mathematics · Physics and Astronomy · #37J35 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2012.02244

openalex publication_date 2020/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Jürgen Moser, we then show that the system is completely integrable, in the sense that the 2N-dimensional system has N 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.

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