Geodesic
Solitary pulse solutions of a coupled nonlinear Schrödinger system arising in optics
Serdica Mathematical Journal, Tome 43 (2017) no. 1, pp. 049-064.

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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.
Keywords: nonlinear Schrödinger, solitary pulse solutions, optics, concentration compactness, existence, 35A15, 35C08, 35Q51, 35Q55 
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     title = {Solitary pulse solutions of a coupled nonlinear {Schr\"odinger} system arising in optics},
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Silwal, Sharad. Solitary pulse solutions of a coupled nonlinear Schrödinger system arising in optics. Serdica Mathematical Journal, Tome 43 (2017) no. 1, pp. 049-064. http://geodesic.mathdoc.fr/item/SMJ2_2017_43_1_a3/