  The Bethe-Salpeter equations for the collective modes of a $t$-$U$-$V$-$J$
model are used to analyze the resonance peak observed at $\bf{Q}=(\pi,\pi)$ in
neutron scattering experiments on the cuprates. We assume that the resonance
emerges due to the mixing between the spin channel and 19 other channels. We
have calculated the energy of the lowest mode of the extended Hubbard model
($J=0$) vs the on-site repulsive interaction $U$, as well as the $UJ$ lines in
the interaction parameter space which are consistent with the ARPES data and
reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the
resonance is predominantly a spin exciton.
