Justification of mean-field coupled modulation equations

Royal Society of Edinburgh - Proceedings A

Volumn 127, Issue 3, 1997, Pages 639-650

  Schneider, Guido ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747017391     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500029942     Document Type: Article

References (27)

1. P. Bollerman. On the validity of amplitude equations. (Thesis, University of Utrecht, 1996).
2. P. Bollerman, A. van Harten and G. Schneider. On the justification of the Ginzburg-Landau approximation. In Nonlinear Dynamics and Pattern Formation in the Natural Environment, eds A. Doelman and A. van Harten, 20-36 (Harlow: Longman, 1995).
3. P. Chossat and G. Iooss. The Taylor-Couette Problem, Applied Mathematical Sciences 102 (New York: Springer, 1994).
4. P. Collet and J.-P. Eckmann. The time dependent amplitude equation for the Swift-Hohenberg problem. Comm. Math. Phys. 132 (1990), 139-53.
5. P. Coullet, S. Fauve and E. Tirapegui. Large-scale instability of nonlinear standing waves. J. Phys. Lett. 46 (1985), L787-L791.
6. G. Dangelmayr. Ginzburg-Landau description of waves in extended systems (Preprint, Universität Tübingen, 1993);
7. in Dynamics of Nonlinear Waves in Dissipative Systems: Reduction, Bifurcation, and Stability, Pitman Research Notes in Mathematics Series (Harlow: Longman, 1996).
8. W. Eckhaus. The Ginzburg-Landau equation is an attractor. J. Nonlinear Sci. 3 (1993), 329-48.
9. W. Eckhaus and A. Shepeleva. Attraction properties of the Ginzburg-Landau manifold (Preprint 878, University of Utrecht, 1994).
10. D. Henry. Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840 (Berlin: Springer, 1981).
11. P. Kirrmann, G. Schneider and A. Mielke. The validity of modulation equations for extended systems with cubic nonlinearities. Proc. Roy. Soc. Edinburgh Sect. A 122 (1992), 85-91.
12. E. Knobloch. Nonlocal amplitude equations. In Pattern Formation in Complex Dissipative Systems, eds S. Kai, 263-74 (Singapore: World Scientific, 1992).
13. E. Knobloch and J. DeLuca. Amplitude equations for travelling wave correction. Nonlinearity 3 (1990), 975-80.
14. E. Knobloch and J. D. Gibbon. Coupled NLS equations for counter propagating waves in systems with reflectional symmetry. Phys. Lett. A 154 (1991), 353-6.
15. B. J. Matkowsky and V. Volpert. Coupled Ginzburg-Landau equations in gasless combustion. Phys. D 54 (1992), 203-19.
16. A. Mielke and G. Schneider. Attractors for modulation equations on unbounded domains - existence and comparison. Nonlinearity 8 (1995), 743-68.
17. A. Newell and J. Whitehead. Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38 (1969), 279-303.
18. C. A. Pereira and J. M. Vega. On the pulsating instability of two-dimensional flames. European J. Appl. Math. 3 (1992), 55-73.
19. R. D. Pierce and E. Knobloch. On the modulational stability of traveling and standing waves. Phys. Fluids 6 (1994), 1177-90.
20. R. D. Pierce and C. E. Wayne. On the validity of mean-field amplitude equations for counter-propagating wavetrains. Nonlinearity 8 (1995), 769-79.
21. G. Schneider. A new estimate for the Ginzburg-Landau approximation on the real axis. J. Nonlinear Sci. 4 (1994), 23-34.
22. G. Schneider. Error estimates for the Ginzburg-Landau approximation. J. Appl. Math. Phys. (ZAMP) 45 (1994), 433-57.
23. G. Schneider. Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations. Comm. Math. Phys. 164 (1994), 157-79.
24. G. Schneider. Analyticity of Ginzburg-Landau modes. J. Differential Equations 121 (1995), 233-57.
25. G. Schneider. The long wave limit for a Boussinesq equation (IfAM Preprint, Universität Hannover, 1995).
26. A. van Harten. On the validity of Ginzburg-Landau's equation. J. Nonlinear Sci. 1 (1991), 397-422.
27. J. M. Vega. On the amplitude equations arising at the onset of the oscillatory instability. SIAM J. Math. Anal. 24 (1993), 603-17.