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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, D95440 Bayreuth, Germany Univ Bayreuth Bayreuth Germany D95440 t Phys, D95440 Bayreuth, Germany
 Titolo Testata:
 PHYSICA D
fascicolo: 12,
volume: 137,
anno: 2000,
pagine: 124  142
 SICI:
 01672789(20000301)137:12<124:TSOSWW>2.0.ZU;23
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 GINZBURGLANDAU EQUATIONS; DEGENERATE HOPF BIFURCATIONS; NEMATIC LIQUIDCRYSTAL; WEAK ELECTROLYTE MODEL; OSCILLATORY INSTABILITY; SPATIOTEMPORAL CHAOS; AMPLITUDE EQUATIONS; PATTERNFORMATION; TRAVELING WAVES; O(2) SYMMETRY;
 Keywords:
 standing wave; Eckhaus; Benjamin Feir instability; counterpropagating 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, D95440 Bayreuth, Germany Univ Bayreuth POB 101251 Bayreuth Germany D95440 euth, Germany



 Citazione:
 H. Riecke e L. Kramer, "The stability of standing waves with small group velocity", PHYSICA D, 137(12), 2000, pp. 124142
Abstract
We determine the modulational stability of standing waves with small groupvelocity in quasionedimensional systems slightly above the threshold of a supercritical Hopf bifurcation, The stability Limits are given by two different longwavelength destabilization mechanisms and generically also a shortwavelength destabilization. The Eckhaus parabola is shifted offcenter and can be convex from below or above. For nonzero Velocity the Newell criterion, which near the crossover from standing to traveling waves becomes a rather weak condition, does not determine the destabilisation of all standing waves in one dimension. The crossover to the nonlocal 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 counterpropagating waves and the wave number selection by sources. Our results yield necessary conditionsfor the stability of traveling rectangles in quasitwodimensional systemswith axial anisotropy and form a starting point for understanding the spatiotemporal chaos of traveling oblique rolls observed in electroconvection of nematic liquid crystals, (C) 2000 Elsevier Science B.V. All rights reserved.
ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 07/08/20 alle ore 00:23:37