Solitary pulse solutions of a coupled nonlinear Schrödinger system arising in optics

We prove the existence of travelling-wave solutions for a system of coupled nonlinear Schrödinger equations arising in nonlinear optics. Such a system describes second-harmonic generation in optical materials with $χ^{(2)}$ 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.

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