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

Abstract

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 ${\chi }^{(2)}$ 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.

References in corpus (1)

• Existence of bound states for (N+1)-coupled long-wave--short-wave interaction equations