  The Dynamical-gap formation in Weyl semimetals modulated by intense
elliptically polarized light is addressed through the solution of the
time-dependent Schr\"odinger equation for the Weyl Hamiltonian via the Floquet
theorem. The time-dependent wave functions and the quasi-energy spectrum of the
two-dimensional Weyl Hamiltonian under normal incidence of elliptically
polarized electromagnetic waves are obtained using a non-perturbative approach.
In it, the Weyl equation is reduced to an ordinary second-order differential
Mathieu equation. It is shown that the stability conditions of the Mathieu
functions are directly inherited by the wave function resulting in a
quasiparticle spectrum consisting of bands and gaps determined by dynamical
diffraction and resonance conditions between the electron and the
electromagnetic wave. Estimations of the electromagnetic field intensity and
frequency, as well as the magnitude of the generated gap are obtained for the
$8-Pmmn$ phase of borophene. We provide with a simple method that enables to
predict the formation of dynamical-gaps of unstable wave functions and their
magnitudes. This method can readily be adapted to other Weyl semimetals.
