  We consider one-dimensional (1D) spin-1/2 fermions in a clean quantum wire,
with forward scattering interactions and a non-linear single-particle spectrum,
$\xi_k = v|k| + k^2/2m$ where $v$ is the Fermi velocity and $1/m$ is the
band-curvature. We calculate the dynamical structure factor (DSF) of the model
at small wave-vector $q$ with the help of the bosonization technique. For
spinless fermions, we show that, starting from the single-parametric spectrum:
$\om = u |q|$, bosonization emulates the 2-parametric excitation spectrum: $\om
= u |q| \pm q^2/2m^*$, where $m^*$ decreases with increasing repulsive
interactions. Moreover, away from the excitation-cone, {\it i.e.} $\om \gg u
|q|$, bosonization yields the 2-pair excitation continuum of the DSF. For
spinful fermions, we show that the spin-charge coupling (SCC) due to
band-curvature affects charge and spin DSF in an asymmetric way. For the charge
DSF, SCC manifests as a two-peak structure: a charge peak at $\om = u_\rho |q|$
but also a spin peak at $\om = u_\sigma |q|$, as charge fluctuations may decay
via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as
a continuous transfer of magnetic spectral weight to frequencies $\om >
u_\sigma |q|$, as spin fluctuations decay via pairs of chargeless spin and
spinless charge-neutral excitations.
