The stability of standing waves with small group velocity

Physica D: Nonlinear Phenomena

Volumn 137, Issue 1-2, 2000, Pages 124-142

  Riecke, Hermann ^a   Kramer, Lorenz ^b  

^a Northwestern University   (United States)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Benjamin Feir instability; Counter propagating waves; Eckhaus; Hopf bifurcation; Standing wave

Indexed keywords

EID: 0347945244     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00123-2     Document Type: Article

References (35)

1. M. Cross, P. Hohenberg, Rev. Mod. Phys. 65 (1993) 851.
2. A. Newell, in: A. Newell (Ed.), Nonlinear Wave Motion, vol. 15, American Mathematical Society, Providence, RI, 1974, p. 157.
3. J. Stuart, R. DiPrima, Proc. R. Soc. London A 362 (1978) 27.
4. B. Matkowsky, V. Volpert, Q. Appl. Math. 51 (1993) 265.
5. M.S. Miguel, Phys. Rev. Lett. 75 (1995) 425.
6. P. Coullet, S. Fauve, E. Tirapegui, J. Physique Lett. 46 (1985) 747.
7. H. Sakaguchi, Prog. Theoret. Phys. 93 (1995) 491.
8. E. Knobloch, in: A. Doelman, A. van Harten (Eds), Nonlinear Dynamics and Pattern Formation in the Natural Environment, Longman, New York, 1995.
9. E. Knobloch, J.D. Luca, Nonlinearity 3 (1990) 975.
10. E. Knobloch, in: S. Kai (Ed.), Pattern Formation in Complex Dissipative Systems, World Scientific, Singapore, 1992.
11. B. Matkowsky, V. Volpert, Physica D 54 (1992) 203.
12. J. Vega, SIAM J. Math. Anal. 24 (1993) 603.
13. C. Martel, J. Vega, Nonlinearity 9 (1996) 1129.
14. C. Martel, J. Vega, Nonlinearity 11 (1998) 105.
15. H. Riecke, Europhys. Lett. 11 (1990) 213.
16. I. Rehberg, G. Ahlers, in: Contemporary Mathematics, vol. 56, 1986.
17. T. Clune, E. Knobloch, Phys. Rev. E 47 (1993) 2536.
18. L. Kramer, W. Pesch, in: A. Buka, L. Kramer (Eds.), Pattern Formation in Liquid Crystals, Electrodydrodynamic Instabities in Nematic Liquid Crystals, Springer, New York, 1996.
19. M. Dennin, D. Cannell, G. Ahlers, Mol. Cryst. Liq. Cryst. 261 (1995) 337.
20. M. Dennin, G. Ahlers, D. Cannel, science 272 (1996) 388.
21. M. Dennin, D. Cannell, G. Ahlers, Phys. Rev. E 57 (1998) 638.
22. M. Silber, H. Rieck, L. Kramer, Physica D 61 (1992) 260.
23. M. Treiber, L. Kramer, Mol. Cryst. Liq. Cryst. 261 (1995) 311.
24. M. Dennin et al., Phys. Rev. Lett. 76 (1996) 319.
25. M. Treiber, N. Eber, A. Buka, L. Kramer, J. Phys. II 7 (1997) 649.
26. M. Treiber, L. Kramer, Phys. Rev. E 58 (1998) 1973.
27. M. Treiber, H. Riecke, L. Kramer, unpublished.
28. I. Aranson, L. Aranson, L. Kramer, A. Weber, Phys. Rev. A 46 (1992) 1992.
29. A. Weber, L. Kramer, I. Aranson, L. Aranson, Physica D 61 (1992) 279.
30. J. Crawford, E. Knobloch, Physica D 31 (1988) 1.
31. M. Golubitsky, M. Roberts, J. Differential Equations 69 (1987) 216.
32. H. Riecke, I. Aranson, unpublished.
33. B. Malomed, Phys. Rev. E 50 (1994) 3310.
34. M. van Hecke, E. Storm, W van Saarloos, Physica D 134 (1999) 1.
35. A. Amengual, E. Hernández-García, R. Montagne, M. San Miguel, Phys. Rev. Lett. 78 (1997) 4379.