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Derivation of the amplitude equation for reaction-diffusion systems via computer-aided multiple-scale expansion. (English) Zbl 1300.35061

MSC:

35K57 Reaction-diffusion equations
35B32 Bifurcations in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
35-04 Software, source code, etc. for problems pertaining to partial differential equations

Software:

Amp_solving; Maple
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Full Text: DOI

References:

[1] DOI: 10.1103/PhysRevE.62.1778
[2] DOI: 10.1364/OPEX.12.003481
[3] DOI: 10.1016/j.jtbi.2008.11.008 · Zbl 1400.92573
[4] DOI: 10.1103/PhysRevE.54.261
[5] DOI: 10.1002/9780470141687.ch5
[6] DOI: 10.1103/RevModPhys.71.S396
[7] DOI: 10.1103/PhysRevE.50.2802 · Zbl 1062.76511
[8] Haragus M., Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems (2010)
[9] DOI: 10.1126/science.1169973
[10] DOI: 10.1016/S0045-7949(99)00184-4
[11] DOI: 10.1143/PTP.63.1152 · Zbl 1059.35513
[12] Klepel K., Zeitschrift für Angewandte Mathematik und Physik pp 98– (2013)
[13] DOI: 10.1016/0375-9601(95)00568-N · Zbl 1020.35510
[14] DOI: 10.1007/s11071-005-2804-1 · Zbl 1142.74345
[15] DOI: 10.1103/PhysRevE.69.066141
[16] Nicolis G., Self-Organization in Nonequilibrium Systems, From Dissipative Structures to Order through Fluctuations (1977) · Zbl 0363.93005
[17] Ozer M. N., Turkish J. Math. 22 pp 309– (1998)
[18] DOI: 10.1103/PhysRevE.64.056213
[19] DOI: 10.1209/epl/i2000-00352-3
[20] DOI: 10.1016/j.jmaa.2004.12.026 · Zbl 1108.35049
[21] DOI: 10.1142/S0218127496001430 · Zbl 1298.35180
[22] DOI: 10.1142/S0218127499000717 · Zbl 1089.37533
[23] DOI: 10.1103/PhysRevE.76.011916
[24] DOI: 10.1007/s11571-012-9194-0
[25] DOI: 10.1088/1674-1056/17/11/003
[26] DOI: 10.1098/rstb.1952.0012 · Zbl 1403.92034
[27] Walgraef D., Spatio-Temporal Pattern Formation: With Examples from Physics, Chemistry, and Materials Science (2012) · Zbl 0871.76003
[28] DOI: 10.1063/1.1507110
[29] Yang L., Phys. Rev. Lett. 88 pp 208– (2002)
[30] DOI: 10.1006/jsvi.1997.1347 · Zbl 1235.34126
[31] DOI: 10.1006/jsvi.2001.3732 · Zbl 1237.70085
[32] DOI: 10.1023/A:1017993026651 · Zbl 0994.65140
[33] DOI: 10.2528/PIER05051701
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