Destabilization and localization of traveling waves by an advected field

Physica D: Nonlinear Phenomena

Volumn 156, Issue 1-2, 2001, Pages 19-38

  Roxin, Alex ^a   Riecke, Hermann ^a  

^a Northwestern University   (United States)

Author keywords

Ginzburg Landau equation; Long wave mode; Short wave instability; Traveling waves

Indexed keywords

EID: 0035427172     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00272-X     Document Type: Article

References (18)

1. F. Charru P. Bartelet Secondary instabilities of interfacial waves due to coupling with a long-wave mode in a two-layer Couette flow Physica D 125 1999 311
2. B.A. Malomed Patterns produced by a short-wave instability in the presence of a zero mode Phys. Rev. A 45 1992 1009
3. H. Riecke Self-trapping of traveling-wave pulses in binary mixture convection Phys. Rev. Lett. 68 1992 301
4. H. Riecke Ginzburg–Landau equation coupled to a concentration field in binary-mixture convection Physica D 61 1992 253 259
5. M. Ipsen P.G. Soerensen Finite wavelength instabilities in a slow mode coupled complex Ginzburg–landau equation Phys. Rev. Lett. 84 2000 2389 2392
6. P.C. Matthews S.M. Cox Pattern formation with a conservation law Nonlinearity 13 2000 1293 1320
7. P. Bartelet F. Charru Benjamin–Feir and Eckhaus instabilities with Galilean invariance: the case of interfacial waves in viscous shear flows Eur. J. Mech. B 17 1998 1 18
8. M. Renardy Y. Renardy Derivation of amplitude equations and analysis of sideband instabilities in two-layer flows Phys. Fluids 5 1993 2738
9. A. Bernoff Finite amplitude convection between stress-free boundaries: Ginzburg–Landau equations and modulation theory Eur. J. Appl. Math. 5 1994 267
10. E.D. Siggia A. Zippelius Pattern selection in Rayleigh–Bénard convection near threshold Phys. Rev. Lett. 47 1981 835
11. F.H. Busse E.W. Bolton Instabilities of convection rolls with stress-free boundaries near threshold J. Fluid Mech. 146 1984 115 125
12. P. Kolodner Drifting pulses of traveling-wave convection Phys. Rev. Lett. 66 1991 1165
13. W. Barten M. Lücke M. Kamps Localized traveling-wave convection in binary fluid mixtures Phys. Rev. Lett. 66 1991 2621
14. H. Riecke G.D. Granzow Localization of waves without bistability: worms in nematic electroconvection Phys. Rev. Lett. 81 1998 333
15. M. Dennin G. Ahlers D.S. Cannell Chaotic localized states near the onset of electroconvection Phys. Rev. Lett. 77 1996 2475
16. P.C. Matthews S.M. Cox One-dimensional pattern formation with Galilean invariance near a stationary bifurcation Phys. Rev. E 62 2 2000 R1473
17. H. Riecke Solitary waves under the influence of a long-wave mode Physica D 92 1996 69 94
18. C. Martel J.M. Vega Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability Nonlinearity 11 1998 105