On The Open Toda Chain with External Forcing

Percy Deift; Luen Chau Li; Herbert Spohn; Carlos Tomei; Thomas Trogdon

On The Open Toda Chain with External Forcing

Percy Deift, Luen Chau Li, Herbert Spohn, Carlos Tomei, Thomas Trogdon

TUM Emeriti of Excellence

Research output: Contribution to journal › Article › peer-review

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 Jurgen Moser, we then show that the system is completely integrable, in the sense that the 27V-dimcnsional 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.

Original language	English
Pages (from-to)	915-945
Number of pages	31
Journal	Pure and Applied Functional Analysis
Volume	7
Issue number	3
State	Published - 2022

Keywords

Action-angle variables
Liouville integrability
Toda lattice
Wave operator

Cite this

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AB - 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 Jurgen Moser, we then show that the system is completely integrable, in the sense that the 27V-dimcnsional 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.

KW - Action-angle variables

KW - Liouville integrability

KW - Toda lattice

KW - Wave operator

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On The Open Toda Chain with External Forcing

Abstract

Keywords

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