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Nonlinear MHD waves in a dissipative plasma with Hall dispersion and the modified Burgers—Schrödinger equation

Published online by Cambridge University Press:  13 March 2009

Sergei V. Korsunsky
Sergei V. Korsunsky
Affiliation:
Institute of Theoretical Physics, Ukrainian Academy of Sciences, 252130, Kiev-130, Ukraine
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Abstract

We consider the nonlinear propagation of magnetosonic waves along an unperturbed magnetic field in a plasma of high but finite conductivity when the Hall effect is taken into account, and we give a discussion of the analytical solutions of the nonlinear evolution equation that governs the latter problem. This equation is a generalization of the well-known modified Schrödinger equation and of the modified Burgers equation (it is referred to here as the modified Burgers-Schrödinger equation). Explicit analytical expressions for both a stationary kink-type solution and circularly polarized quasi-periodic waves are obtained and investigated.

Type
Research Article
Information
Journal of Plasma Physics , Volume 48 , Issue 2 , October 1992 , pp. 237 - 243
Copyright
Copyright © Cambridge University Press 1992

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References

Baranov, V. B. & Ruderman, M. S. 1974 Soviet Phys. Mech. Liq. Gas 3. 108.Google Scholar
Brio, M. 1987 Wave Motion 9, 455.CrossRefGoogle Scholar
Chen, F. F. 1984 Introduction to Plasma Physics and controlled Fusion. Plenum.CrossRefGoogle Scholar
Frenzen, C. L. & Kevorkian, J. 1985 Wave Motion 7, 25.CrossRefGoogle Scholar
Johnson, R. S. 1970 J. Fluid Mech. 42, 49.CrossRefGoogle Scholar
Jeffrey, A. & Mohamad, M. N. B. 1991 Wave Motion 14, 369.CrossRefGoogle Scholar
Khanna, M. & Rajaram, R. 1982 J. Plasma Phys. 16, 321.Google Scholar
Korsunsky, S. V. 1990 Math. Meth. Phys. Math. Fields 32, 73.Google Scholar
Lee-Bapty, J. P. & Crighton, D. G. 1987 Phil. Trans. R. Soc. Lond. A 323, 137.Google Scholar
Mjolhus, E. 1974 Department of Applied Mathematics, University of Bergen, Report 48.Google Scholar
Mjolhus, E. 1976 J. Plasma Phys. 16, 321.CrossRefGoogle Scholar
Mjolhfs, E. 1978 J. Plasma Phys. 19, 437.Google Scholar
Porkolab, M. & Chang, R. P. H. 1978 Rev. Mod. Phys. 50, 745.Google Scholar
Sachdev, P. L. 1987 Nonlinear Diffusive Waves. Cambridge University Press.CrossRefGoogle Scholar
Shah, H. A. & Bruno, R. 1987 J. Plasma Phys. 37, 143.CrossRefGoogle Scholar
Shercliff, J. 1965 A Textbook of Magnetohydrodynamics. Pergamon.Google Scholar