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Oblique nonlinear Alfvén waves in strongly magnetized beam plasmas. Part 2. Soliton solutions and integrability

Published online by Cambridge University Press:  13 March 2009

Bernard Deconinck ,
Peter Meuris  and
Frank Verheest
Bernard Deconinck
Affiliation:
Sterrenkundig Observatorium, Universiteit Gent, Krijslaan 281, B-9000 Gent, Belgium
Peter Meuris
Affiliation:
Sterrenkundig Observatorium, Universiteit Gent, Krijslaan 281, B-9000 Gent, Belgium
Frank Verheest
Affiliation:
Sterrenkundig Observatorium, Universiteit Gent, Krijslaan 281, B-9000 Gent, Belgium
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Abstract

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 50 , Issue 3 , December 1993 , pp. 457 - 476
Copyright
Copyright © Cambridge University Press 1993

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References

Belinfante, J. G. F. & Kolman, B. 1989 A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods 2nd edn.SIAM.CrossRefGoogle Scholar
Braun, M. 1983 Differential Equations and Their Applications. Springer.Google Scholar
Deconinck, B., Meuris, P. & Verheest, F. 1993 J. Plasma Phys. 50, 445.CrossRefGoogle Scholar
Fordy, A. 1990 Soliton Theory: A Survey of Results (ed. Fordy, A.), p. 403. Manchester University Press.Google Scholar
Griffiths, J. B. 1985 The Theory of Classical Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Hada, T., Kennel, C. F. & Buti, B. 1989 J. Geophys. Res. 94, 65.CrossRefGoogle Scholar
Kaup, D. J. 1980 Physica D 1, 391.Google Scholar
Kaup, D. J. & Newell, A. C. 1978 J. Math. Phys. 19, 798.CrossRefGoogle Scholar
Kennel, C. F., Buti, .B, Hada, T. & Pellat, R. 1988 Phys. Fluids 31, 1949.CrossRefGoogle Scholar
Kawata, T. & Inoue, H. 1978 J. Phys. Soc. Japan 44, 1968.CrossRefGoogle Scholar
Mjølhus, E. 1989 Physica Scripta 40, 227.CrossRefGoogle Scholar
Spangler, S. R. & Plapp, B. B. 1992 Phys. Fluids B 4, 3356.CrossRefGoogle Scholar