Speed-of-light pulses in a nonlinear Weyl equation

TL;DR

This paper introduces a nonlinear Weyl equation and demonstrates that certain pulse solutions propagate at the speed of light, maintaining their shape, with potential implications for physics and photonics.

Contribution

The study presents the first analysis of pulse dynamics in a nonlinear Weyl equation, showing shape-preserving, light-speed propagation of localized pulses in multiple dimensions.

Findings

Localized pulses split into two-hump structures

Pulses move at the speed of light or Fermi velocity

Exact solutions for specific nonlinearities are identified

Abstract

We introduce a prototypical nonlinear Weyl equation, motivated by recent developments in massless Dirac fermions, topological semimetals and photonics. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two-hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a transient time $t_s$ this pulse moves with the speed of light (or Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics and maintaining its shape (both in two and three dimensions). We show that for the considered nonlinearity, this pulse represents an exact solution of the nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the results to a broader class of nonlinearities and on their emerging potential for observation in different areas of application.