  The quantum modes of a nonlinear Klein-Gordon lattice have been computed
numerically [L. Proville, Phys. Rev. B 71, 104306 (2005)]. The on-site
nonlinearity has been found to lead to phonon bound states. In the present
paper, we compute numerically the dynamical structure factor so as to simulate
the coherent scattering cross section at low temperature. The inelastic
contribution is studied as a function of the on-site anharmonicity.
Interestingly, our numerical method is not limited to the weak anharmonicity
and permits one to study thoroughly the spectra of nonlinear phonons.
