Solar Physics

, Volume 105, Issue 2, pp 265–289 | Cite as

Long nonlinear waves in a compressible magnetically structured atmosphere

III. Fast sausage waves in a magnetic slab
  • E. G. Merzljakov
  • M. S. Ruderman
Article

Abstract

The Hohlov-Zabolotskaja equation with an additional boundary condition is shown to describe long nonlinear small-amplitude fast sausage surface waves in a magnetic slab embedded in magnetic environment. It is proved that the obtained boundary problem has no solutions in the form of solitary waves. Approximate solution in the form of nonlinear stationary wave is found with the use of expansion in the power series of small amplitude. Second harmonic generation by a sinusoidal wave is studied. The law of energy conservation is obtained. Results of numerical computations are presented. They show that a sinusoidal disturbance does not overturn. The possibility of transmission of wave energy into corona along a magnetic slab is discussed in connection with these results.

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References

  1. Bahvalov, N. S., Žileikin, Ja. M., and Zabolotskaja, E. A.: 1982, Nelineinaja teorija zvukovyh puchkov, Nauka, Moscow.Google Scholar
  2. Edwin, P. M. and Roberts, B.: 1982, Solar Phys. 76, 239.Google Scholar
  3. Gradstein, I. S. and Ryzik, I. M.: 1962, Tablicy integralov, summ, rjadov i proizvedenii, Fizmatgiz, Moscow.Google Scholar
  4. Hollweg, J. V. and Roberts, B.: 1984, J. Geophys. Res. 89, No. A11, 9703.Google Scholar
  5. Korn, G. and Korn, T.: 1961, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Co. Inc., New York.Google Scholar
  6. Merzljakov, E. G. and Ruderman, M. S.: 1985, Solar Phys. 95, 51.Google Scholar
  7. Merzljakov, E. G. and Ruderman, M. S.: 1986, Solar Phys., in press.Google Scholar
  8. Roberts, B.: 1981, Solar Phys. 69, 39.Google Scholar
  9. Roberts, B.: 1983, in J. O. Stenflo (ed.), ‘Solar and Stellar Magnetic Fields: Origins and Coronal Effects’, IAU Symp. 102.Google Scholar
  10. Roberts, B.: 1984, 6th Gen. Conf. of European Phys. Soc. ‘Trends in Physics’, Prague, invited review.Google Scholar
  11. Roberts, B.: 1985, Phys. Fluids 28, 3280.Google Scholar
  12. Roberts, B. and Mangeney, A.: 1982, Monthly Notices Roy. Astron. Soc. 198, 7P.Google Scholar
  13. Rudenko, O. V. and Solujan, S. I.: 1977, Theoretical Foundations of Nonlinear Acoustics, Plenum Publ. Corporation, Consultants Bureau, New York and London.Google Scholar
  14. Ruderman, M. S.: 1985, Izv. Akad. Sci. USSR, M.J.G., No. 1, 98.Google Scholar
  15. Samarskii, A. A.: 1983, Teorija raznostnyh shem, Nauka, Moscow.Google Scholar
  16. Zabolotskaja, E. A. and Hohlov, R. V.: 1969, Akusticheskii Zh. 15, 40.Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • E. G. Merzljakov
    • 1
  • M. S. Ruderman
    • 1
  1. 1.Space Research Institute, Academy of Sciences of USSRMoscowU.S.S.R.

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