  The Hubbard model provides a simple framework in which one can study how
certain aspects of the electronic structure of strongly interacting systems can
be tuned to optimize the superconducting pairing correlations and how these
changes affect the mechanisms giving rise to them. Here we use a weak-coupling
random phase approximation to study a two-dimensional Hubbard model with a
unidirectional modulation of the hopping amplitudes as the system evolves from
the uniform square lattice to an array of weakly coupled two-leg ladders. We
find that the pairing correlations retain their dominant $d_{x^2-y^2}$-wave
like structure and that they are significantly enhanced for a slightly
modulated lattice. This enhancement is traced backed to an increase in the
strength of the spin-fluctuation pairing interacting due to favorable Fermi
surface nesting in the modulated system. We then use a random-phase
approximation BCS framework to examine the evolution of the neutron resonance
in the superconducting state. We find that it changes only weakly for moderate
modulations, but breaks up into two distinct resonances at incommensurate
wave-vectors in the limit of weakly coupled ladders.
