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

Speed-of-light pulses in a nonlinear Weyl equation