  We initiate the perturbative study of the S-matrix for the excitations on top
of the GKP vacuum at strong coupling. Using the string sigma model action
expanded around the null cusp classical solution, we compute the tree-level
S-matrix elements and compare them with the predictions from the asymptotic
Bethe Ansatz. We also check the factorization of the three-body S-matrix for
various bosonic processes, finding precise agreement with the constraints
imposed by integrability.
