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Moving modulating pulse and front solutions of permanent form in a FPU model with nearest and next-to-nearest neighbor interaction

Hilder, Bastian; de Rijk, Björn; Schneider, Guido

Abstract:
We consider a nonlinear chain of coupled oscillators, which is a direct generalization of the classical FPU lattice and exhibits, besides the usual nearest neighbor interaction, also next-to-nearest neighbor interaction. For the case of nearest neighbor attraction and next-to-nearest neighbor repulsion we prove that such a lattice admits, in contrast to the classical FPU model, moving modulating front solutions of permanent form, which have small converging tails at infinity and can be approximated by solitary wave solutions of the Nonlinear Schrödinger equation. When the associated potentials are even, then the proof yields moving modulating pulse solutions of permanent form, whose profiles are spatially localized. Our analysis employs the spatial dynamics approach as developed by Iooss and Kirchgässner. The relevant solutions are constructed on a five-dimensional center manifold and their persistence is guaranteed by reversibility arguments.


Volltext §
DOI: 10.5445/IR/1000139214
Veröffentlicht am 26.10.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 10.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000139214
Verlag KIT, Karlsruhe
Umfang 38 S.
Serie CRC 1173 Preprint ; 2021/42
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter Fermi-Pasta-Ulam lattice, next-to-nearest neighbor interaction, moving modulating pulse and front solution, spatial dynamics, center manifold reduction, normal form
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