  Several nonlinear spectroscopy experiments which employ broadband x-ray
pulses to probe the coupling between localized core and delocalized valence
excitation are simulated for the amino acid cysteine at the K-edges of oxygen
and nitrogen and the K and L-edges of sulfur. We focus on two dimensional (2D)
and 3D signals generated by two- and three-pulse stimulated x-ray Raman
spectroscopy (SXRS) with frequency-dispersed probe. We show how the four-pulse
x-ray signals
$\boldsymbol{k}_\mathrm{I}=-\boldsymbol{k}_1+\boldsymbol{k}_2+\boldsymbol{k}_3$
and
$\boldsymbol{k}_\mathrm{II}=\boldsymbol{k}_1-\boldsymbol{k}_2+\boldsymbol{k}_3$
can give new 3D insight into the SXRS signals. The coupling between valence-
and core-excited states can be visualized in three dimensional plots, revealing
the origin of the polarizability that controls the simpler pump-probe SXRS
signals.
