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Failure of the $N$-wave interaction approximation without imposing periodic boundary conditions

Haas, Tobias; Schneider, Guido


The N-wave interaction (NWI) system appears as an amplitude system in the description of N nonlinearly interacting and linearly transported wave packets in dispersive wave systems, such as the water wave problem or problems in nonlinear optics. The purpose of this paper is twofold. First we give a new simplified proof for the failure of the NWI approximation in case of resonances which are located at integer multiples of a basic wave number k_0 in the original dispersive wave system. Secondly, we give a first rigorous proof that an amplitude system fails in the description of an original system, without imposing periodic boundary conditions on the original system.

Volltext §
DOI: 10.5445/IR/1000088285
Veröffentlicht am 05.12.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000088285
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 25 S.
Serie CRC 1173 ; 2018/41
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagwörter counter example, no approximation, TWI, new proof
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