  We prove the existence of travelling-wave solutions for a system of coupled
nonlinear Schr\"{o}dinger equations arising in nonlinear optics. Such a system
describes second-harmonic generation in optical materials with $\chi^{(2)}$
nonlinearity. To prove the existence of travelling waves, we employ the method
of concentration compactness to prove the relative compactness of minimizing
sequences of the associated variational problem.
