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The Bethe-Salpeter equations for the collective modes of a $t$-$U$-$V$-$J$model are used to analyze the resonance peak observed at $\bf{Q}=(\pi,\pi)$ inneutron scattering experiments on the cuprates. We assume that the resonanceemerges due to the mixing between the spin channel and 19 other channels. Wehave 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 inthe interaction parameter space which are consistent with the ARPES data andreproduces the resonance peak at 40 meV in Bi2212 compound. We find that theresonance is predominantly a spin exciton.

Bethe-Salpeter equations for the collective modes of the $t-U-V-J$ model with d-wave pairing