Abstract
Electron acoustic blow up solitary waves and periodic waves are studied in a classical unmagnetized plasma containing cold electron fluid, kappa distributed hot electrons and stationary ions. We obtain Korteweg-de Vries (KdV) equation for electron acoustic waves (EAWs) using the reductive perturbation technique (RPT). Applying bifurcation theory of planar dynamical systems to the obtained KdV equation, we prove the existence of electron acoustic blowup solitary and periodic wave solutions. Depending on different physical parameters, two types of exact explicit solutions of the mentioned waves are derived. Our model may be applied to explain blow up solitary and periodic wave features that may occur in the planetary magnetosphere and the plasma sheet boundary layer.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anowar, M.G., Mamun, A.A.: Phys. Plasmas 15, 102111 (2008)
Berthomier, M., Pottelette, R., Malingre, M., Khotyainsev, Y.: Phys. Plasmas 7, 2987 (2000)
Berthomier, M., Pottelette, R., Muschietti, L., Roth, I., Carlson, C.W.: Geophys. Res. Lett. 30, 2148 (2003)
Byrd, P.F., Friedman, M.D.: Handbook of Elliptic Integrals for Engineer and Scientists. Springer, New York (1971)
Chow, S.N., Hale, J.K.: Method of Bifurcation Theory. Springer, New York (1981)
Dell, M.P., Geldhill, I.M.A., Hellberg, M.A.: Z. Naturforsch. A, J. Phys. Sci. 42, 1175 (1987)
Derfler, H., Simonen, T.C.: Phys. Fluids 12, 269 (1969)
Dubouloz, N., Pottelette, R., Malingre, M., Holmgren, G., Lindqvist, P.A.: J. Geophys. Res. 96, 3565 (1991)
Dubouloz, N., Trueman, R.A., Pottelette, R., Malingre, M.: J. Geophys. Res. 98, 17415 (1993)
El-Labany, S.K., Shalaby, M., Sabry, R., El-Sherif, L.S.: Astrophys. Space Sci. 340, 101 (2012)
El-Wakil, S.A., Abulwafa, E.M., El-shewy, E.K., Mahmoud, A.A.: Astrophys. Space Sci. 333, 269 (2011)
Franz, J.R., Kintner, P.M., Pickett, J.S.: Geophys. Res. Lett. 25, 1277 (1998)
Fried, B.D., Gould, R.W.: Phys. Fluids 4, 139 (1961)
Gary, S.P., Tokar, R.L.: Phys. Fluids 28, 2439 (1985)
Ghosh, S.S., Sen, A., Lakhina, G.S.: Nonlinear Process. Geophys. 9, 463 (2002)
Guckenheimer, J., Holmes, P.J.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York (1983)
Ikezawa, S., Nakamura, Y.: J. Phys. Soc. Jpn. 50, 962 (1981)
Lakhina, G.S., Kakad, A.P., Singh, S.V., Verheest, F.: Phys. Plasmas 15, 062903 (2008a)
Lakhina, G.S., Singh, S.V., Kakad, A.P., Verheest, F., Bharuthram, R.: Nonlinear Process. Geophys. 15, 903 (2008b)
Lin, C.S., Burch, J.L., Shawhan, S.D., Gurnett, D.A.: J. Geophys. Res. 89, 925 (1984). doi:10.1029/JA089iA02p00925
Mace, R.L., Baboolal, S., Bharuthram, R., Hellberg, M.A.: J. Plasma Phys. 45, 323 (1991)
Mamun, A.A., Shukla, P.K.: J. Geophys. Res. 107, 1135 (2002)
Mannan, A., Mamun, A.A.: Astrophys. Space Sci. 340, 109 (2012)
Masood, W., Shah, H.A.: J. Fusion Energy 22, 201 (2003)
Matsumoto, H., Kojima, H., Miyatake, T., Omura, Y., Okada, M., Nagano, I., Tsutsui, M.: Geophys. Res. Lett. 21, 2915 (1994). doi:10.1029/94GL01284
Pottelette, R., Ergun, R.E., Treumann, R.A., Berthomier, M., Carlson, C.W., McFadden, J.P., Roth, I.: Geophys. Res. Lett. 26, 2629 (1999)
Saha, A., Chatterjee, P.: Astrophys. Space Sci. 349, 239 (2014a)
Saha, A., Chatterjee, P.: Astrophys. Space Sci. 349, 813 (2014b)
Samanta, U.K., Saha, A., Chatterjee, P.: Phys. Plasmas 20, 052111 (2013a)
Samanta, U.K., Saha, A., Chatterjee, P.: Phys. Plasmas 20, 022111 (2013b)
Samanta, U.K., Saha, A., Chatterjee, P.: Astrophys. Space Sci. 347, 293 (2013c)
Schriver, D., Ashour-Abdalla, M.: Geophys. Res. Lett. 16, 899 (1989)
Shah, A., Rakha, A.: Astrophys. Space Sci. 344, 113 (2013)
Shalaby, M., El-Labany, S.K., Sabry, R., El-Sherif, L.S.: Phys. Plasmas 18, 062305 (2011)
Singh, S.V., Lakhina, G.S.: Planet. Space Sci. 49, 107 (2001)
Singh, S.V., Lakhina, G.S.: Nonlinear Process. Geophys. 11, 275 (2004a)
Singh, S.V., Lakhina, G.S.: Nonlinear Process. Geophys. 11, 275 (2004b)
Singh, S.V., Reddy, R.V., Lakhina, G.S.: Adv. Space Res. 28, 1643 (2001)
Shukla, P.K., Mamun, A.A., Eliasson, B.: Geophys. Res. Lett. 31, L07803 (2004)
Thomsen, M.F., Barr, H.C., Gary, S.P., Feldman, W.C., Cole, T.E.: J. Geophys. Res. 88, 3035 (1983). doi:10.1029/JA088iA04p03035
Tribeche, M., Sabry, R.: Astrophys. Space Sci. 341, 579 (2012)
Tsurutani, B.T., Arballo, J.K., Lakhina, G.S., Ho, C.M., Buti, B., et al.: Geophys. Res. Lett. 25, 4117 (1998)
Verheest, F., Cattaert, T., Hellberg, M.A.: Space Sci. Rev. 121, 299 (2005)
Watanabe, K., Taniuti, T.: J. Phys. Soc. Jpn. 43, 1819 (1977)
Yu, M., Shukla, P.K.: J. Plasma Phys. 29, 409 (1983)
Acknowledgements
This work is partially supported by DST, India under (D.O. no: SR/S2/HEP-32/2012). The authors are really grateful to the reviewers for their useful comments and suggestions which helped to improve the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Saha, A., Chatterjee, P. Electron acoustic blow up solitary waves and periodic waves in an unmagnetized plasma with kappa distributed hot electrons. Astrophys Space Sci 353, 163–168 (2014). https://doi.org/10.1007/s10509-014-2030-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-014-2030-8