Nonlinear Ritz method and the motion of defects
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 2, pp. 202-214 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider certain special dissipative systems having important physical applications. We construct approximate solutions describing the motion of defects and systems of defects. We develop a moving-defect interaction theory and calculate the friction force produced by the system of defects.
Keywords: dissipative system, approximate solution, kink, kink interaction
Mots-clés : friction.
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A. K. Abramyan; S. A. Vakulenko. Nonlinear Ritz method and the motion of defects. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 2, pp. 202-214. http://geodesic.mathdoc.fr/item/TMF_2008_155_2_a1/

[1] G. Nikolis, I. Prigozhin, Samoorganizatsiya v neravnovesnykh sistemakh, Mir, M., 1979 | MR | Zbl

[2] G. Khaken, Sinergetika, Mir, M., 1980 | MR | Zbl

[3] Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer, Berlin, 1984 | MR | Zbl

[4] O. A. Ladyzhenskaya, UMN, 42:6 (1987), 25–60 | MR | Zbl

[5] J. K. Hale, Asymptotic Behavior of Dissipative Systems, AMS, Providence, RI, 1988 | MR | Zbl

[6] A. V. Babin, M. I. Vishik, J. Math. Pures Appl., 62 (1983), 441–491 | MR | Zbl

[7] P. Constantin, C. Foias, B. Nicolaenko, R. Temam, Integral Manifolds and Inertial Manifolds for Dissipative Differential Equations, Springer, New York, 1989 | MR | Zbl

[8] Yu. Ilyashenko, Veigu Li, Nelokalnye bifurkatsii, MTsNMO, CheRo, M., 1999 | MR | MR | Zbl

[9] P. Poláčik, “Parabolic equations: asymptotical behaviour on invariant manifolds”, Handbook of Dynamical Systems, vol. 2, ed. B. Fiedler, North-Holland, Amsterdam, 2002, 835–883 | MR | Zbl

[10] S. A. Vakulenko, Ann. Inst. H. Poincarè Phys. Théor., 66 (1997), 373–410 | MR | Zbl

[11] S. A. Vakulenko, Adv. Differential Equations, 5:7–9 (2000), 1139–1178 | MR | Zbl

[12] S. A. Vakulenko, P. V. Gordon, Arch. Mech., 5:5 (1999), 547–558 | MR | Zbl

[13] N. Achmediev, J. M. Soto-Crespo, G. Town, Phys. Rev. E, 63:5 (2001), 6602 | DOI

[14] N. Achmediev, A. Ankiewicz, “Dissipative solitons in the complex Ginzburg–Landau and Swift–Hohenberg equations”, Dissipative Solitons, Lecture Notes in Phys., 661, eds. N. Akhmediev, A. Ankievicz, Springer, Berlin, 2005, 1–17 | DOI | MR | Zbl

[15] A. B. Vasileva, V. F. Butuzov, Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vysshaya shkola, M., 1990 | MR | Zbl

[16] A. B. Vasileva, V. F. Butuzov, N. N. Nefedov, Avtomatika i telemekhanika, 1997, no. 7, 4–32 | MR | Zbl

[17] S. Yu. Dobrokhotov, V. P. Maslov, “Konechnozonnye pochti periodicheskie resheniya v VKB-priblizheniyakh”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 15, VINITI, M., 1980, 3–94 | MR | Zbl

[18] S. Yu. Dobrokhotov, I. M. Krichever, Matem. zametki, 49:6 (1991), 42–58 | DOI | MR | Zbl

[19] I. A. Molotkov, S. A. Vakulenko, Sosredotochennye nelineinye volny, Izd-vo LGU, L., 1988 | MR

[20] V. F. Butuzov, A. B. Vasilieva, Adv. Chem. Phys., 97 (1997), 47–179 | DOI

[21] A. B. Vasileva, V. F. Butuzov, N. N. Nefedov, Fundament. i prikl. matem., 4:3 (1998), 799–851 | MR | Zbl

[22] J. Carr, R. L. Pego, Comm. Pure Appl. Math., 42:5 (1989), 523–576 | DOI | MR | Zbl

[23] G. Fusco, “A genetic approach to the analysis of $u_t=\epsilon^2u_{xx}+f(u)$ for small $\epsilon$”, Problems Involving Change of Type (Stuttgart, 1988), Lecture Notes in Phys., 359, ed. K. Kirchgässner, Springer, Berlin, 1990, 53–73 | DOI | MR | Zbl

[24] V. F. Butuzov, N. N. Nefedov, K. R. Schneider, J. Differential Equations, 159:2 (1999), 427–446 | DOI | MR | Zbl

[25] A. L. Korgenevskii, R. Bausch, R. Schmitz, Phys. Rev. Lett., 83:22 (1999), 4578–4581 | DOI