Validity of the nonlinear Schr "odinger approximation for quasilinear\n dispersive systems with more than one derivative

2020/05/05 by Max Heß, Heß, Max
Physics and Astronomy · #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2005.02051

openalex publication_date 2020/05/05 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

For nonlinear dispersive systems, the nonlinear Schr "odinger (NLS) equation\ncan usually be derived as a formal approximation equation describing slow\nspatial and temporal modulations of the envelope of a spatially and temporally\noscillating underlying carrier wave. Here, we justify the NLS approximation for\na whole class of quasilinear dispersive systems, which also includes toy models\nfor the waterwave problem. This is the first time that this is done for\nsystems, where a quasilinear quadratic term is allowed to effectively lose more\nthan one derivative. With effective loss we here mean the loss still present\nafter making a diagonalization of the linear part of the system such that all\nlinear operators in this diagonalization have the same regularity properties.\n

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