Speed-of-light pulses in a nonlinear Weyl equation

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.

7 pages, 6 figures

References in corpus (5)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates
• Weyl solitons in three-dimensional optical lattices
• Solitary waves in the Nonlinear Dirac Equation
• Speed-of-light pulses in the massless nonlinear Dirac equation with a potential

Cited by in corpus (3)

• Self-localized topological states in three dimensions
• Nonlinearity and Topology
• Solitary wave solutions of the 2+1 and 3+1 dimensional nonlinear Dirac equation constrained to planar and space curves