Instability of the steady states of some Ginzburg-Landau-like equations with real coefficients

Nonlinearity

Volumn 18, Issue 4, 2005, Pages 1425-1441

  Vega, José M ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21244494017     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/4/001     Document Type: Article

References (34)

1. Newell A and Whitehead J 1969 Finite bandwith, finite amplitude convection J. Fluid Mech. 38 279-304
2. Cross M C and Hohenberg P C 1993 Pattern formation outside of equilibrium Rev. Mod. Phys. 65 851-1112
3. Knobloch E and De Luca J 1990 Amplitude equations for travelling wave convection Nonlinearity 3 55-73
4. Alvarez-Pereira C and Vega J M 1992 On the pulsating instability of two-dimensional flames Eur. J. Appl. Math. 3 55-73
5. Vega J M 1993 On the amplitude equations arising at the onset of the oscillatory instability in pattern formation SIAM J. Math. Anal. 24 603-17
6. Martel C and Vega J M 1996 Finite size effects near the onset of the oscillatory instability Nonlinearity 9 1129-71
7. Elmer F J 1988 Nonlinear and nonlocal dynamics of spatially extended systems: stationary states, bifurcations and stability Physica D 30 321-42
8. Faraday M 1831 On the forms and states assumed by fluids in contact with vibrating elastic surfaces Phil. Trans. R. Soc. Lond. 121 319-40
9. Lord Rayleigh J W S 1883 On the crispations of fluid resting upon a vibrating support Phil. Mag. 16 50-8
10. Miles J and Henderson D 1990 Parametrically forced surface waves Ann. Rev. Fluid Mech. 22 143-65
11. Fauve S 1995 Parametric instabilities Dynamics of Nonlinear and Disordered Systems ed G Martínez Mekler and T H Seligman (Singapore: World Scientific) pp 67-115
12. Mancebo F J and Vega J M 2004 Viscous Faraday waves in 2D large aspect ratio containers Preprint
13. Martel C, Knobloch E and Vega J M 2000 Dynamics of counterpropagating waves in parametrically forced systems Physica D 137 94-123
14. Mancebo F J and Vega J M 2004 Standing wave description of nearly conservative, parametrically driven waves in extended systems Physica D 197 346-63
15. Vega J M, Knobloch E and Martel C 2001 Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio Physica D 154 313-36
16. Lapuerta V, Martel C and Vega J M 2002 Weakly-dissipative Faraday waves in 2D large aspect ratio annuli Physica D 173 178-203
17. Coullet P and Iooss G 1990 Instabilities of one-dimensional cellular patterns Phys. Rev. Lett. 64 866-9
18. Matthews P C and Cox S M 2000 Pattern formation with a conservation law Nonlinearity 13 1293-320
19. Matthews P C and Cox S M 2001 New instabilities in two-dimensional rotating convection and magnetoconvection Physica D 149 210-29
20. Weidman P D, Linde H and Velarde M G 1992 Evidence of solitary wave behavior in Marangoni-Bénard convection Phys. Fluids A 4 921-6
21. Golovin A A, Nepomnyashkchy A A and Pismen L M 1993 Interaction between short-scale Marangoni convection and long-scale deformational instability Phys. Fluids 6 34-48
22. Plaut E and Busse F H 2002 Low Prandtl number convection in a rotating cylindrical annulus J. Fluid Mech. 464 345-63
23. Tanaka D and Kuramoto Y 2003 Complex Ginzburg-Landau equation with nonlocal coupling Phys. Rev. E 68 026219
24. Kramer L and Zimmermann W 1985 On the Eckhaus instability for spatially periodic patterns Physica D 16 221-32
25. Doelman A, Gardner R A and Jones C K R T 1995 Instability of quasiperiodic solutions of the Ginzburg-Landau equation Proc. R. Soc. Edinb. A 125 501-17
26. Norbury J, Wei J and Winter M 2002 Existence and stability of singular patterns in a Ginzburg-Landau equation coupled with a mean field Nonlinearity 15 2077-96
27. Henry D 1989 Geometric Theory of Semilinear Parabolic Equations (Berlin: Springer)
28. Ladyženskaja O A, Solonnikov V A and Ural'ceva N N 1968 Linear and Quasilinear Equations of Parabolic Type (Providence, RI: American Mathematical Society)
29. Adams R A 1975 Sobolev Spaces (New York: Academic)
30. Hale J K 1989 Asymptotic Behavior of Dissipative Systems (Providence, RI: American Mathematical Society)
31. Coddington E A and Levinson N 1955 Theory of Ordinary Differential Equations (New York: McGraw-Hill)
32. Dieudonné J 1960 Foundations of Modern Analysis (New York: Academic)
33. Courant R and Hilbert D 1962 Methods of Mathematical Physics vol I and II (New York: Wiley, Interscience)
34. Kreyszig E 1978 Introductory Functional Analysis with Applications (New York: Wiley)