Justification of the Coupled Mode Asymptotics for Localized Wavepackets\n in the Periodic Nonlinear Schr "odinger Equation

2016/02/12 by Tomáš Dohnal, Dohnal, Tomáš, Lisa Helfmeier +1
Computer Science · Physics and Astronomy · #35C07 #35C20 #35Q55 #35Q60 #41A60 #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.1602.04121

openalex publication_date 2016/02/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We consider wavepackets composed of two modulated carrier Bloch waves with\nopposite group velocities in the one dimensional periodic Nonlinear\nSchroedinger/Gross-Pitaevskii equation. These can be approximated by first\norder coupled mode equations (CMEs) for the two slowly varying envelopes. Under\na suitably selected periodic perturbation of the periodic structure the CMEs\npossess a spectral gap of the corresponding spatial operator and allow families\nof exponentially localized solitary waves parametrized by velocity. This leads\nto a family of approximate solitary waves in the periodic nonlinear\nSchroedinger equation. Besides a formal derivation of the CMEs a rigorous\njustification of the approximation and an error estimate in the supremum norm\nare provided. Several numerical tests corroborate the analysis.\n

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