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Titolo:
The stability of standing waves with small group velocity
Autore:
Riecke, H; Kramer, L;
Indirizzi:
Northwestern Univ, Dept Engn Sci & Appl Math, Evanston, IL 60208 USA Northwestern Univ Evanston IL USA 60208 Appl Math, Evanston, IL 60208 USA Univ Bayreuth, Inst Phys, D-95440 Bayreuth, Germany Univ Bayreuth Bayreuth Germany D-95440 t Phys, D-95440 Bayreuth, Germany
Titolo Testata:
PHYSICA D
fascicolo: 1-2, volume: 137, anno: 2000,
pagine: 124 - 142
SICI:
0167-2789(20000301)137:1-2<124:TSOSWW>2.0.ZU;2-3
Fonte:
ISI
Lingua:
ENG
Soggetto:
GINZBURG-LANDAU EQUATIONS; DEGENERATE HOPF BIFURCATIONS; NEMATIC LIQUID-CRYSTAL; WEAK ELECTROLYTE MODEL; OSCILLATORY INSTABILITY; SPATIOTEMPORAL CHAOS; AMPLITUDE EQUATIONS; PATTERN-FORMATION; TRAVELING WAVES; O(2) SYMMETRY;
Keywords:
standing wave; Eckhaus; Benjamin Feir instability; counter-propagating waves; Hopf bifurcation;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
35
Recensione:
Indirizzi per estratti:
Indirizzo: Kramer, L Univ Bayreuth, Inst Phys, POB 101251, D-95440 Bayreuth, Germany Univ Bayreuth POB 101251 Bayreuth Germany D-95440 euth, Germany
Citazione:
H. Riecke e L. Kramer, "The stability of standing waves with small group velocity", PHYSICA D, 137(1-2), 2000, pp. 124-142

Abstract

We determine the modulational stability of standing waves with small groupvelocity in quasi-one-dimensional systems slightly above the threshold of a supercritical Hopf bifurcation, The stability Limits are given by two different long-wavelength destabilization mechanisms and generically also a short-wavelength destabilization. The Eckhaus parabola is shifted off-center and can be convex from below or above. For non-zero Velocity the Newell criterion, which near the cross-over from standing to traveling waves becomes a rather weak condition, does not determine the destabilisation of all standing waves in one dimension. The cross-over to the non-local and the hyperbolic equations that are asymptotically valid near threshold is discussed indetail. Close to thr transition from standing to traveling waves complex dynamics can arise due to the competition of counter-propagating waves and the wave number selection by sources. Our results yield necessary conditionsfor the stability of traveling rectangles in quasi-two-dimensional systemswith axial anisotropy and form a starting point for understanding the spatio-temporal chaos of traveling oblique rolls observed in electroconvection of nematic liquid crystals, (C) 2000 Elsevier Science B.V. All rights reserved.

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Documento generato il 07/08/20 alle ore 00:23:37