  We investigate the dynamical spin structure factor S(q,w) for the Heisenberg
chain with ferromagnetic nearest (J1<0) and antiferromagnetic next-nearest
(J2>0) neighbor exchange using bosonization and a time-dependent density-matrix
renormalization group algorithm. For |J1|<< J2 and low energies we analytically
find and numerically confirm two spinon branches with different velocities and
different spectral weights. Following the evolution of S(q,w) with decreasing
J1/J2 we find that helimagnons develop at high energies just before entering
the ferromagnetic phase. Furthermore, we show that a recent interpretation of
neutron scattering data for LiCuVO4 in terms of two weakly coupled
antiferromagnetic chains (|J_1|<< J2) is not viable. We demonstrate that the
data are instead fully consistent with a dominant ferromagnetic coupling, J1/J2
~ -2.
