Propagation of well-prepared states along Martinet singular geodesics

TL;DR

This paper demonstrates that in a subelliptic wave equation with a flat Martinet metric, singularities can propagate at any speed between 0 and 1 along singular geodesics, contrasting with classical wave equations.

Contribution

It establishes the novel result that singularities in the Martinet wave equation propagate at variable speeds along singular geodesics, unlike the fixed speed in elliptic cases.

Findings

Singularities propagate at any speed between 0 and 1

Propagation occurs along singular geodesics

Contrasts with classical wave propagation at speed 1

Abstract

We prove that for the Martinet wave equation with "flat" metric, which a subelliptic wave equation, singularities can propagate at any speed between 0 and 1 along any singular geodesic. This is in strong contrast with the usual propagation of singularities at speed 1 for wave equations with elliptic Laplacian.