On the Spatial Asymptotics of Solutions of the Toda Lattice

TL;DR

This paper studies the long-distance behavior of solutions to the Toda lattice, showing that their asymptotic form remains constant over time and that disturbances can propagate infinitely fast.

Contribution

It demonstrates the preservation of asymptotic behavior and establishes infinite propagation speed in the Toda lattice, advancing understanding of its long-term dynamics.

Findings

Asymptotic behavior is preserved over time.

Leading asymptotic term remains time-independent.

Infinite propagation speed is established.

Abstract

We investigate the spatial asymptotics of decaying solutions of the Toda hierarchy and show that the asymptotic behaviour is preserved by the time evolution. In particular, we show that the leading asymptotic term is time independent. Moreover, we establish infinite propagation speed for the Toda lattice.