Localized states in the generalized Swift-Hohenberg equation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 5, 2006, Pages

  Burke, John ^a   Knobloch, Edgar ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONTROL NONLINEARITIES; EQUATIONS OF STATE; NUMERICAL METHODS; STABILITY;

CUBIC NONLINEARITIES; LOCALIZED STATES; NUMERICAL COMPUTATIONS; SWIFT-HOHENBERG EQUATION;

NONLINEAR EQUATIONS;

EID: 33744829750     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.056211     Document Type: Article

References (47)

1. S. Fauve and O. Thual, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.282 64, 282 (1990).
2. K. Kirchgässner, J. Differ. Equations JDEQAK 0022-0396 10.1016/0022-0396(82)90058-4 45, 113 (1982).
3. G. Iooss and M. C. Perouème, J. Differ. Equations JDEQAK 0022-0396 10.1006/jdeq.1993.1022 102, 62 (1993).
4. Y. Pomeau, Physica D PDNPDT 0167-2789 10.1016/0167-2789(86)90104-1 23, 3 (1986).
5. M. F. Hilali, S. Métens, P. Borckmans, and G. Dewel, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.51.2046 51, 2046 (1995).
6. P. Coullet, C. Riera, and C. Tresser, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3069 84, 3069 (2000).
7. A. R. Champneys, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00209-1 112, 158 (1998).
8. G. W. Hunt, M. A. Peletier, A. R. Champneys, P. D. Woods, M. Ahmer Wadee, C. J. Budd, and G. J. Lord, Nonlinear Dyn. NODYES 0924-090X 10.1023/A:1008398006403 21, 3 (2000).
9. Y. Nishiura and D. Ueyama, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(99)00010-X 130, 73 (1999).
10. E. Doedel, R. C. Paffenroth, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. E. Oldeman, B. Sandstede, and X. Wang, AUTO97: Continuation and bifurcation software for ordinary differential equations, Concordia University (2002) http://indy.cs.concordia.ca/auto/main.html
11. U. Thiele and E. Knobloch, Physica D PDNPDT 0167-2789 10.1016/j.physd.2003.09.048 190, 213 (2004).
12. D. Bensimon, B. I. Shraiman, and V. Croquette, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.5461 38, 5461 (1988).
13. T.-S. Yang and T. R. Akylas, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112096003643 330, 215 (1997).
14. I. Melbourne, J. Nonlinear Sci. JNSCEK 0938-8794 8, 1 (1998).
15. B. Sandstede, Philos. Trans. R. Soc. London, Ser. A PTRMAD 0962-8428 10.1098/rsta.1997.0111 355, 2083 (1997).
16. These coefficients disagree with those given by P. D. Woods and A. R. Champneys, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(98)00309-1 129, 147 (1999).
17. C. J. Budd and R. Kuske, Physica D PDNPDT 0167-2789 208, 73 (2005).
18. J. Burke and E. Knobloch (unpublished).
19. P. Coullet, C. Riera, and C. Tresser, Chaos CHAOEH 1054-1500 10.1063/1.1642311 14, 193 (2004).
20. I. S. Aranson, B. A. Malomed, L. M. Pismen, and L. S. Tsimring, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.R5 62, R5 (2000).
21. J. Knobloch and T. Wagenknecht, Physica D PDNPDT 0167-2789 206, 82 (2005).
22. D. Gomila, A. J. Scroggie, and W. J. Firth (unpublished).
23. G. H. M. van der Heijden, Dyn. Syst. ZZZZZZ 1468-9367 15, 159 (2000).
24. L. A. Peletier and W. C. Troy, Spatial Patterns: Higher Order Models in Physics and Mechanics (Birkhäuser, Boston, 2001).
25. A. Hagberg, A. Yochelis, H. Yizhaq, C. Elphick, L. Pismen, and E. Meron, Physica D PDNPDT 0167-2789 217, 186 (2006).
26. M. K. Wadee, C. D. Coman, and A. P. Bassom, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(02)00350-0 163, 26 (2002).
27. P. B. Umbanhowar, F. Melo, and H. L. Swinney, Nature (London) NATUAS 0028-0836 10.1038/382793a0 382, 793 (1996).
28. O. Lioubashevski, Y. Hamiel, A. Agnon, Z. Reches, and J. Fineberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3190 83, 3190 (1999).
29. M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.640 73, 640 (1994).
30. A. G. Vladimirov, J. M. McSloy, D. V. Skryabin, and W. J. Firth, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.046606 65, 046606 (2002).
31. J. M. McSloy, W. J. Firth, G. K. Harkness, and G.-L. Oppo, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046606 66, 046606 (2002).
32. R. Richter and I. V. Barashenkov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.184503 94, 184503 (2005).
33. C. R. Laing, W. C. Troy, B. Gutkin, and G. B. Ermentrout, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139901389495 63, 62 (2002).
34. A. Spina, J. Toomre, and E. Knobloch, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.57.524 57, 524 (1998).
35. S. Blanchflower, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(99) 00573-3 261, 74 (1999).
36. S. Blanchflower and N. O. Weiss, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00076-2 294, 297 (2002).
37. O. Batiste and E. Knobloch, Phys. Fluids PHFLE6 1070-6631 10.1063/1.1920349 17, 064102 (2005).
38. O. Batiste and E. Knobloch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.244501 95, 244501 (2005).
39. O. Batiste, E. Knobloch, A. Alonso, and I. Mercader J. Fluid Mech (to be published).
40. J. H. P. Dawes (unpublished).
41. H. Sakaguchi and H. Brand, Physica D PDNPDT 0167-2789 10.1016/0167-2789(96)00077-2 97, 274 (1996).
42. D. Lloyd, Ph.D. thesis, University of Bristol, Bristol.
43. A. R. Champneys and J. F. Toland, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/6/5/002 6, 665 (1993).
44. B. Buffoni, A. R. Champneys, and J. F. Toland, J. Dyn. Differ. Equ. JDDEEH 1040-7294 8, 221 (1996).
45. A. R. Champneys, M. D. Groves, and P. D. Woods, Phys. Lett. A PYLAAG 0375-9601 271, 178 (2000).
46. R. Grimshaw, B. Malomed, and E. Benilov, Physica D PDNPDT 0167-2789 77, 473 (1994).
47. I. V. Barashenkov, S. Cross, and B. A. Malomed, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.056605 68, 056605 (2003).