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Polarized high-frequency wave propagation beyond the nonlinear Schrödinger approximation

Baumstark, Julian 1; Jahnke, Tobias 1; Lubich, Christian
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract:

This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein–Gordon equations and the Maxwell–Lorentz system. The interest here is in solutions that are polarized in the sense that up to a small error, the oscillations in the solution depend on only one of the frequencies that satisfy the dispersion relation with a given wave vector appearing in the initial wave packet. The construction and analysis of such polarized solutions is done using modulated Fourier expansions. This approach includes higher harmonics and yields approximations to polarized solutions that are of arbitrary order in the small parameter, going well beyond the known first-order approximation via a nonlinear Schrödinger equation. The given construction of polarized solutions is explicit, uses in addition a linear Schrödinger equation for each further order of approximation, and is accessible to direct numerical approximation.


Volltext §
DOI: 10.5445/IR/1000148063
Veröffentlicht am 27.06.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 06.2022
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000148063
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 21 S.
Serie CRC 1173 Preprint ; 2022/28
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter semilinear high-frequency wave propagation, modulated Fourier expansions, nonlinear polarization, error analysis
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