zbMATH — the first resource for mathematics

Solitary wave trains in a cold plasma. (English. Russian original) Zbl 0923.76356
Fluid Dyn. 31, No. 5, 754-761 (1996); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza. 1996, No. 5, 154-161 (1996).
Summary: The existence of traveling solitary waves, the products of modulation instability in a cold quasi-neutral plasma, is considered. Solitary waves of this type (“solitary wave trains”) are formed as a result of bifurcation from a nonzero wave number of the linear wave spectrum. It is shown that the complete system of equations describing the wave process in a cold plasma has solutions of the solidary wave train type, at least when the undisturbed magnetic field is perpendicular to the wave front. Sufficient conditions of existence of solitary wave trains in weakly dispersive media are also formulated.
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
Full Text: DOI
[1] T. Kakutani and H. Ono, ”Weak non-linear hydromagnetic waves in a cold collision-free plasma,”J. Phys. Soc. Japan,26, 1305 (1969).
[2] A. Il’ichev, ”Steady waves in a cold plasma,”J. Plasma Phys., (1995).
[3] G. Iooss and M. G. Peroueme, ”Perturbed homoclinic solutions in reversible 1:1 resonance vector fields,”J. Differents. Equat.,102, 62 (1993). · Zbl 0792.34044
[4] G. Iooss and M. Adelmeyer,Topics in Bifurcation Theory and Applications, World Scientific, Singapore (1992). · Zbl 0833.34001
[5] F. Dias and G. Iooss, ”Capillary-gravity solitary waves with damped oscillations,”Physica., D,65, 399 (1993). · Zbl 0778.76014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.