  Studying the scattering of excitations around a dynamical background has a
long history in the context of integrable models. The Gubser-Klebanov-Polyakov
string solution provides such a background for the string/gauge correspondence.
Taking the conjectured all-loop asymptotic equations for the AdS_4/CFT_3
correspondence as the starting point, we derive the S-matrix and a set of
spectral equations for the lowest-lying excitations. We find that these
equations resemble closely the analogous equations for AdS_5/CFT_4, which are
also discussed in this paper. At large values of the coupling constant we show
that they reproduce the Bethe equations proposed to describe the spectrum of
the low-energy limit of the AdS_4xCP^3 sigma model.
