Large time asymptotics of the wave fronts length II: surfaces with integrable Hamiltonians

TL;DR

This paper extends previous results on the large time asymptotics of wave front lengths from the unit disk to integrable 2D Hamiltonian systems, providing a broader understanding of wave propagation in such systems.

Contribution

It generalizes the linear asymptotic formula for wave front lengths to a wider class of integrable 2D Hamiltonian systems, building on prior work.

Findings

Established large time linear asymptotics for wave fronts in integrable 2D Hamiltonian systems

Extended previous results from the unit disk to more general surfaces

Provided a mathematical framework for analyzing wave front growth in integrable systems

Abstract

In a previous work, David Vicente gave a formula showing that the wave front issued of a point of the unit disk hasa large time linear asymptotics. In the present paper, we extend the result to intgrable 2D Hamiltoniansystems.