Advertisement

Geomagnetism and Aeronomy

, Volume 58, Issue 7, pp 947–952 | Cite as

Fast Sausage Solitons and Super Nonlinearity in Coronal Loops

  • Y. Naga VarunEmail author
  • G. A. Mankaeva
  • B. B. Mikhalyaev
Article
  • 12 Downloads

Abstract

We consider fast sausage solitons and super nonlinearity in straight homogeneous magnetic tubes having coronal parameters. The solitonic behavior is described by the Nonlinear Schrödinger Equation-(NLSE) obtained from the ideal magneto hydrodynamic equations with suitable coronal conditions. For the first time we demonstrated that fast sausage waves are subjected to super nonlinearity and likewise introduced the super nonlinear function that defines this phenomenon. We have obtained classical localized sausage soliton and Peregrine sausage breather soliton solutions for coronal conditions. And finally we have carried out extensive numerical simulations of the evolution of a wave packet governed by the NLS equation with real nonlinear parameters and demonstrated the existence and domain of the above mentioned solitonic modes.

Notes

ACKNOWLEDGMENTS

We express our gratitude to Prof. A.A. Solov’ev who happened to be our referee and whose comments helped us to strengthen the scientific rigor of our article.

REFERENCES

  1. 1.
    Aschwanden, M., Physics of the Solar Corona: An Introduction with Problems and Solutions, Springer and Praxis, 2006.Google Scholar
  2. 2.
    Sulem, C. and Sulem, P.-L., The Nonlinear Schrodinger Equation: Self focusing and Wave Collapse, New York: Springer, 1999.Google Scholar
  3. 3.
    Falkovich, G., Fluid Mechanics: A Short Course for Physicists, New York, Cambridge University Press, 2011.CrossRefGoogle Scholar
  4. 4.
    Mikhalyaev, B.B. and Ruderman, M.S., Nonlinear fast sausage waves in homogeneous magnetic flux tubes, J. Plasma Phys., 2015, vol. 81, 905810611.CrossRefGoogle Scholar
  5. 5.
    Mikhalyaev, B.B., Ruderman, M.S., and Naga Varun, E., Nonlinear radial oscillations of the coronal loops, Geomagn. Aeron. (Engl. Transl.), 2016, vol. 56, no. 8, pp. 1040–1044.Google Scholar
  6. 6.
    Peregrine, D.H., Water waves, nonlinear Schrodinger equations and their solutions, J. Aust. Math. Soc. B, 1983, vol. 25, pp. 16–43.CrossRefGoogle Scholar
  7. 7.
    Polyanin, A.D. and Zaitsev, V.F., Handbook of Nonlinear Partial Differential Equations, New York: Chapman and Hall/CRC, 2003.CrossRefGoogle Scholar
  8. 8.
    Stasiewicz, K., Heating of the solar corona by dissipative Alfvén solitons, Phys. Rev. Lett., 2006, vol. 96, 175003.CrossRefGoogle Scholar
  9. 9.
    Zabusky, N.J. and Kruskal, M.D., Interaction of “solitons” in collisionless plasma and the recurrence of initial states, Phys. Rev. Lett., 1965, vol. 15, no. 6, pp. 240–240.CrossRefGoogle Scholar
  10. 10.
    Zaqarashvili, T.V., Kukhianidze, V., and Khodachenko, M.L., Propagation of a sausage soliton in the solar lower atmosphere observed by Hinode/SOT, Mon. Not. R. Astron. Soc., 2010, pp. L74–L78.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Y. Naga Varun
    • 1
    Email author
  • G. A. Mankaeva
    • 1
  • B. B. Mikhalyaev
    • 1
  1. 1.Kalmyk Gorodovikov State UniversityElistaRussia

Personalised recommendations