Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-02T23:30:28.028Z Has data issue: false hasContentIssue false
  • English
  • Français

Modulations of slow sausage surface waves travelling along a magnetized slab

Published online by Cambridge University Press:  13 March 2009

I. Zhelyazko ,
K. Murawski ,
M. Goossens ,
P. Nenovaki  and
B. Roberts
I. Zhelyazko
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
K. Murawski
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
M. Goossens
Affiliation:
Centre for Plasma Astrophysics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
P. Nenovaki
Affiliation:
Institute for Space Research, BG-1000 Sofia, Bulgaria
B. Roberts
Affiliation:
Department of Mathematical and Computational Sciences, University of St Andrews, St Andrews KY16 9SS, Fife, Scotland
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we consider a set of nonlinear MHD equations that admits in a linear approximation a solution in the form of a slow sausage surface wave travelling along an isolated magnetic slab. For a wave of small but finite amplitude, we investigate how a slowly varying amplitude is modulated by nonlinear self-interactions. A stretching transformation shows that, at the lowest order of an asymptotic expansion, the original set of equations with appropriate boundary conditions (free interfaces) can be reduced to the cubic nonlinear Schrödinger equation, which determines the amplitude modulation. We study analytically and numerically the evolution of impulsively generated waves, showing a transition of the initial states into a train of solitons and periodic waves. The possibility of the existence of solitary waves in the solar atmosphere is also briefly discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 51 , Issue 2 , April 1994 , pp. 291 - 308
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ablowitz, M. J. &Segur, H. 1981 Solitons and the Inverse Scattering Transform. SIAM.CrossRefGoogle Scholar
Bogdan, T. J. &Lerche, I. 1988 Q. Appl. Maths 46, 365.CrossRefGoogle Scholar
Cramer, N. F. 1991 J. Plasma Phys. 46, 15.CrossRefGoogle Scholar
Edwin, P.M. &Roberts, B. 1986 Wave Motion 8, 151.CrossRefGoogle Scholar
Fornberg, B. &Whitham, G. B. 1978 Phil. Trans. B. Soc. Lond. A289, 373.Google Scholar
Grozev, D., Shivarova, A. &Boarman, A. D. 1987 J. Plasma Phys. 38, 427.CrossRefGoogle Scholar
Hasegawa, A. 1972 Phys. Fluids 15, 870.CrossRefGoogle Scholar
Hasegawa, A. 1989 Optical Solitons in Fibers. Springer.CrossRefGoogle Scholar
Hasegawa, A. &Tappert, F. 1973 Appl. Phys. Leit. 23, 171.CrossRefGoogle Scholar
Hollweg, J. V. &Roberts, B. 1984 J. Geophys. Res. 89A, 9703.CrossRefGoogle Scholar
Kakutani, T. &Michihiro, K. 1983 J. Phys. Soc. Japan 52, 4129.CrossRefGoogle Scholar
Laedke, E. W. &Spatschek, K. H. 1985 Differential Geometry, Calculus of Variations, and Their Applications (ed. Rassias, G. M. & Rassias, T. M.), p. 335. Dekker.Google Scholar
Matsuno, Y. 1984 Bilinear Transformation Method. Academic.Google Scholar
Merzljakov, E. G. 1985 Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza (Bull. Acad. Sci. USSR, Mech. Liquid and Gas), no. 2, p. 164.Google Scholar
Merljakov, E. G. &Ruderman, M. S. 1985 Solar Phys. 95, 51.CrossRefGoogle Scholar
Merljakov, E. G. &Ruderman, M. S. 1986 a Solar Phys. 103, 259.CrossRefGoogle Scholar
Merljakov, E. G. &Ruderman, M. S. 1986 b Solar Phys. 105, 265.Google Scholar
Mio, K., Ogino, T., Mimami, K. &Takeda, S. 1976 J. Phys. Soc. Japan 41, 265.CrossRefGoogle Scholar
Mjølhus, E. 1978 J. Plasma Phys. 19, 437.CrossRefGoogle Scholar
Murawski, K. 1987 Aust. J. Phys. 40, 593.CrossRefGoogle Scholar
Murawski, K. 1991 Acta Phys. Polon. A80, 495.CrossRefGoogle Scholar
Murawski, K. &Edwin, P. M. 1992 J. Plasma Phys. 47, 75.CrossRefGoogle Scholar
Murawski, K. &Roberts, B. 1993 Solar Phys. 144, 255.CrossRefGoogle Scholar
Murawski, K. &Storer, R. 1989 Wave Motion 41, 309.CrossRefGoogle Scholar
Nouri, F. Z. &Sloan, E. 1989 J. Comp. Phys. 83, 324.CrossRefGoogle Scholar
Parkes, E. J. 1987 a J. Phys. A20, 2025.Google Scholar
Parakes, E. J. 1987 b J. Phys. A20, 3653.Google Scholar
Parthia, D. &Morris, J. L. 1990 J. Comp. Phys. 87, 108.Google Scholar
Roberts, B. 1981 Solar Phys. 69, 39.CrossRefGoogle Scholar
Roberts, B. 1985 Phys. Fluids 28, 3280.CrossRefGoogle Scholar
Roberts, B. 1991 a Mechanisms of Chromospheric and Coronal Heating (ed. Ulmschneider, P., Priest, E. R. & Rosner, R.), p. 494. Springer.CrossRefGoogle Scholar
Roberts, B. 1991 b Advances in Solar System Magnetohydrodynamics (ed. Priest, E. R. & Hood, A. W.), p. 105. Cambridge University Press.Google Scholar
Roberts, B. &Mangeney, A. 1982 Mon. Not. R. Astron. Soc. 198, 7P.CrossRefGoogle Scholar
Ruderman, M. S. 1985 Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza (Bull. Acad. Sci. USSR, Mech. Liquid and Gas), no. 1, p. 98.Google Scholar
Ruderman, M. S. 1988 Plasma Phys. Contr. Fusion 30, 1117.CrossRefGoogle Scholar
Ruderman, M. S. 1991 J. Plasma Phys. 47, 175.CrossRefGoogle Scholar
Ruderman, M. S. 1992 J. Geophys. Res. 97 A, 16843.CrossRefGoogle Scholar
Sahyouni, W., Zhelyazkov, I. &Nenovski, P. 1988 Solar Phys. 115, 17.CrossRefGoogle Scholar
Spruit, H. C. &Roberts, B. 1983 Nature 304, 401.CrossRefGoogle Scholar
Taniuti, T. &Yajima, N. 1969 J. Math. Phys. 10, 1369.CrossRefGoogle Scholar
Weisshaar, E. 1989 Phys. Fluids A1, 1406.CrossRefGoogle Scholar
Zabolotskaya, E. A. &Khokhlov, R. V. 1969 Akoust. Zh. 15, 40.Google Scholar