Solitary waves in a~cold plasma
Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 719-728.

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We study the existence of soliton-like solutions (solitary waves) to the equations describing the one-dimensional motion of a cold quasi-neutral plasma. It is shown that in some range of the angle between the norperturbed magnetic field and the wave propagation direction there exists a branch of solitary hydromagnetic waves that is a bifurcation of the zero wave number. These solutions lie on a two-dimensional center manifold.
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     title = {Solitary waves in a~cold plasma},
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A. T. Il'ichev. Solitary waves in a~cold plasma. Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 719-728. http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a7/

[1] Pliss V. A., “Printsip reduktsii v teorii ustoichivosti dvizheniya”, Izv. AN SSSR. Ser. matem., 28 (1964), 1297–1324 | MR | Zbl

[2] Iooss G., Adelmeyer M., Topics in bifurcation theory and applications, World Scientific, 1992

[3] Kirchgässner K., “Wave solutions of reversible systems and applications”, J. Diff. Equat., 45 (1982), 113–127 | DOI | MR | Zbl

[4] Mielke A., “Reduction of quasilinear elliptic equations in cylindrical domains with applications”, Math. Meth. Appl. Sci., 10 (1988), 51–66 | DOI | MR | Zbl

[5] Mielke A., “Normal hyperbolicity of center manifolds and Saint–Venant's principle”, Arch. Rat. Mech. Anal., 110 (1990), 353–372 | DOI | MR | Zbl

[6] Iooss G., Kirchgässner K., “Water waves for small surface tension: an approach via normal form”, Proc. Royal Soc. Edinburgh, 122A (1992), 267–299 | MR

[7] Saffman P. G., “On hydromagnetic waves of finite amplitude in a cold plasma”, J. Fluid Mech., 11 (1961), 552–566 | DOI | MR | Zbl

[8] Kakutani T., Ono H., Tanuiti T., Wei C.-C., “Reductive perturbation method in nonlinear wave propagation. II: Application to hydromagnetic waves in cold plasma”, J. Phys. Soc. Japan, 24 (1968), 1159–1166 | DOI

[9] Kakutani T., Ono H., “Weak non-linear hydromagnetic waves in a cold collision-free plasma”, J. Phys. Soc. Japan, 26 (1969), 1305–1318 | DOI

[10] Ilichev A. T., “O suschestvovanii semeistva solitonopodobnykh reshenii uravneniya Kavakhary”, Matem. zametki, 52 (1992), 42–50 | MR

[11] Il'ichev A. T., Semenov A. Yu., “Stability of solitary waves in dispersive media described by a fifth order evolution equation”, Theoret. Comput. Fluid Dynamics, 3 (1992), 307–326 | DOI | Zbl

[12] Maslov V. P., Omelyanov G. A., “Vzaimodeistvie korotkikh voln v slabo dispersionnoi plazme, I”, Ukr. matem. zh., 39 (1987), 464–472 | MR