Noncommutative waves have infinite propagation speed

TL;DR

This paper proves the existence of global solutions for noncommutative nonlinear wave equations in even dimensions and demonstrates that these waves propagate instantaneously across space, regardless of initial support.

Contribution

It establishes the existence of solutions without restrictions on nonlinearity degree and reveals infinite propagation speed in noncommutative wave equations.

Findings

Global solutions exist in arbitrary even dimensions.

Noncommutative waves have infinite propagation speed.

No restrictions on nonlinearity degree for existence.

Abstract

We prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there are no conditions on the degree of the nonlinearity provided the potential is positive. We furthermore prove that nonlinear noncommutative waves have infinite propagation speed, i.e., if the initial conditions at time 0 have a compact support then for any positive time the support of the solution can be arbitrarily large.