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The validity of the Derivative NLS approximation for systems with cubic nonlinearities

Heß, Max 1; Schneider, Guido 1
1 Universität Stuttgart (Uni Stuttgart)

Abstract:

The (generalized) Derivative Nonlinear Schrödinger (DNLS) equation can be derived as an envelope equation via multiple scaling perturbation analysis from dispersive wave systems. It occurs when the cubic coefficient for the associated NLS equation vanishes for the spatial wave number of the underlying slowly modulated wave packet. It is the purpose of this paper to prove that the DNLS equation makes correct predictions about the dynamics of a Klein-Gordon model with a cubic nonlinearity. The proof is based on energy estimates and normal form transformations. New difficulties occur due to a total resonance and due to a second order resonance.


Volltext §
DOI: 10.5445/IR/1000152646
Veröffentlicht am 16.11.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Universität Stuttgart (Uni Stuttgart)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 14.11.2022
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000152646
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 33 S.
Serie CRC 1173 Preprint ; 2022/58
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
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