  We explain the effects of superconductivity on the incommensurate magnetic
response $\chi''(q,\omega)$ observed in inelastic neutron scattering
measurements on La$_{2-x}$Sr$_x$CuO$_4$. We show that a spin-fermion model
correctly describes the frequency and momentum dependent changes of $\chi''$ in
the superconducting phase. We find these changes are generic features of an
incommensurate spin structure and the d-wave symmetry of the superconducting
gap and are thus expected for all cuprates with an incommensurate magnetic
response. Our analysis of INS experiments in La$_{2-x}$Sr$_x$CuO$_4$ up to
optimal doping suggests a Fermi surface which is closed around $(\pi,\pi)$.
