  The dynamical spin structure factor is computed within a variational
framework to study the one-dimensional $J_1-J_2$ Heisenberg model. Starting
from Gutzwiller-projected fermionic wave functions, the low-energy spectrum is
constructed from two-spinon excitations. The direct comparison with Lanczos
calculations on small clusters demonstrates the excellent description of both
gapless and gapped (dimerized) phases, also including incommensurate structures
for $J_2/J_1>0.5$. Calculations on large clusters show how the intensity
evolves when increasing the frustrating ratio and give an unprecedented
accurate characterization of the dynamical properties of (non-integrable)
frustrated spin models.
