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Year 2018, Volume: 8 Issue: 2, 438 - 447, 01.12.2018

Abstract

References

  • Washimi, H. and Taniuti, T.(1966)Propagation of ion-acoustic solitary waves of small amplitude, Phys. Rev. Lett.,17, 996-998.
  • Tribeche, M. and Sabry,R.(2012) Electron-acoustic solitary waves in a magnetized plasma with hot electrons featuring Tsallis distribution, Astrophys. Space Sci., 341, 579-85.
  • Bostrom, R.(1992) Observation of weak double layers on auroral field lines, IEEE Trans. Plasma Sci., , 756-763.
  • Dovner, P.,Erikson, E.,Bostrom, R.and Holback, B.(1994) Freja multiprobe observations of electro- static solitary structures, Geophys. Res. Lett., 21, 1827-1830.
  • Cairn, R., Mamun, A., Bingham, R. ,Bostrom, R., Dendy, R., Nairn, C.and Shukla, P.(1995) Electro- statics solitary structures in nonthermal plasmas, J. Geophys. Res., 22, 2709-2712.
  • C. Tsallis, C. (1988)Possible generalization of Boltzman-Gibbs statistics, J. Statistical Physics, 52, 487.
  • Tribeche, M.,Djebarni, L. and Armour, R.(2010)Ion-acoustic solitary waves in a plasma with a q- nonextensive electron velocity distribution, Phys. Plasmas, 17, 042114.
  • N. Akhtar, N.,El-Taibany, W. and Mahmoud, S.(2013) Electrostatic double layers in a warm negative ion plasma with non-extensive electrons, Phys. Lett. A, 377, 1282-1289.
  • Tribeche, M., Amour, R. and Shukla, P. K. (2012) Ion acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution, Phys. Rev. E, 85, 037401.
  • Amour, R., Tribeche, M. and Shukla,P. K.(2012) Electron-acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution, Asrophys. Space Sci. 338, 287-294.
  • Wang, Y. Y., Li, J. T.,Dai, C. Q.,Chen, X. F. and Zhang,Z. F.(2013) Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution, Phys. Lett. A ,377, 2097-2014.
  • Bouzit, O., Gougam, L. A. and Tribeche, M.(2014) Solitons and freak waves in a mixed nonextensive high energy-tail electron distribution, Phys. Plasmas, 21, 062101
  • Bouzit, O.,Tribeche, M. and Bains, A. S.(2015) Modulational instability of ion-acoustic waves in a plasma with a q-nonextensive nonthermal electron velocity distribution, Phys. Plasmas, 22,084506.
  • Ikezi, H., Taylor,R. and Baker, D.(1970)Formation and interaction of ion-acoustic solitons, Phys. Rev. Lett. 25, 11-14 .
  • Ikezi, H.(1973)Experiments on ion-acoustic solitary waves, Phys. Fluids, 16, 1668-167.
  • Kato,Y., Tajiri, M. and Taniuti, T.(1972) Precursor of ion-acoustic quasishock wave in collisionless plasma, Phys. Fluids, 15, 865-870.
  • Taniuti, T.(1974) Reductive perturbation method and far fields of wave equations,Suppl. of Progress in Theoretical Phys., 55, 1-35.
  • N. Sugimoto and T. Kakutani, Note on the higher order terms in reductive perturbation theory, J. Phys. Soc. Japan, 43, 1469-1470 (1977).
  • Kodama, Y. and Taniuti, T.(1978) Higher order perturbation in the reductive perturbation method
  • I:Weakly dispersive systems, J. Phys. Soc. Japan, 45, 298-310. Malfliet, M. and Wieers, E.(1999) Theory of ion-acoustic waves re-visited, J. Plasma Phys., 56, 441
  • Demiray, H.(1999) A modified reductive perturbation method as applied to nonlinear ion-acoustic waves, J. Phys. Soc. Japan, 68, 1833-1837.
  • Demiray, H.(2012) Contribution of higher order terms in the nonlinear shallow water waves, TWMS J. Appl. Engr. Math., 2, 210-218.
  • Williams, G., Kourakis, I., Verheest, F. and Hellberg, M. A.(2013) Re-examining the Cairns-Tsallis model for ion acoustic solitons, Physical Review E, 88, 023103.
  • Hilmi Demiray, for a photograph and biography, see TWMS Journal of Applied and Engineering Mathematics, Volume 1, No.1, 2011.

HIGHER ORDER PERTURBATION EXPANSION FOR ION-ACOUSTIC SOLITARY WAVES WITH Q-NONEXTENSIVE NONTHERMAL VELOCITY DISTRIBUTION

Year 2018, Volume: 8 Issue: 2, 438 - 447, 01.12.2018

Abstract

The basic nonlinear equations describing the dynamics of a two component plasma consisting of cold positive ions and electrons obeying hybrid q- nonextensive non-thermal velocity distribution are examined through the use of modi ed PLK formalism and the reductive perturbation method and obtained the KdV equation for the lowest order term in the perturbation expansion. The method is further extended to include the contribution of higher order terms in the expansion; the evolution equation for the second order term is found to be the degenerate linearized KdV equation with non- homogeneous term. Seekink the localized travelling wave solution solitons to these evolution equations we obtained the speed correction terms and the wave pro les. Nu-merical results for the set of suitable parameters Williams et. al. [23] are shown inb the form of some graphs. The combined e ect of nonextensive parameter q and the nonthermal parameter on the soliton dynamics has also been studied.

References

  • Washimi, H. and Taniuti, T.(1966)Propagation of ion-acoustic solitary waves of small amplitude, Phys. Rev. Lett.,17, 996-998.
  • Tribeche, M. and Sabry,R.(2012) Electron-acoustic solitary waves in a magnetized plasma with hot electrons featuring Tsallis distribution, Astrophys. Space Sci., 341, 579-85.
  • Bostrom, R.(1992) Observation of weak double layers on auroral field lines, IEEE Trans. Plasma Sci., , 756-763.
  • Dovner, P.,Erikson, E.,Bostrom, R.and Holback, B.(1994) Freja multiprobe observations of electro- static solitary structures, Geophys. Res. Lett., 21, 1827-1830.
  • Cairn, R., Mamun, A., Bingham, R. ,Bostrom, R., Dendy, R., Nairn, C.and Shukla, P.(1995) Electro- statics solitary structures in nonthermal plasmas, J. Geophys. Res., 22, 2709-2712.
  • C. Tsallis, C. (1988)Possible generalization of Boltzman-Gibbs statistics, J. Statistical Physics, 52, 487.
  • Tribeche, M.,Djebarni, L. and Armour, R.(2010)Ion-acoustic solitary waves in a plasma with a q- nonextensive electron velocity distribution, Phys. Plasmas, 17, 042114.
  • N. Akhtar, N.,El-Taibany, W. and Mahmoud, S.(2013) Electrostatic double layers in a warm negative ion plasma with non-extensive electrons, Phys. Lett. A, 377, 1282-1289.
  • Tribeche, M., Amour, R. and Shukla, P. K. (2012) Ion acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution, Phys. Rev. E, 85, 037401.
  • Amour, R., Tribeche, M. and Shukla,P. K.(2012) Electron-acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution, Asrophys. Space Sci. 338, 287-294.
  • Wang, Y. Y., Li, J. T.,Dai, C. Q.,Chen, X. F. and Zhang,Z. F.(2013) Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution, Phys. Lett. A ,377, 2097-2014.
  • Bouzit, O., Gougam, L. A. and Tribeche, M.(2014) Solitons and freak waves in a mixed nonextensive high energy-tail electron distribution, Phys. Plasmas, 21, 062101
  • Bouzit, O.,Tribeche, M. and Bains, A. S.(2015) Modulational instability of ion-acoustic waves in a plasma with a q-nonextensive nonthermal electron velocity distribution, Phys. Plasmas, 22,084506.
  • Ikezi, H., Taylor,R. and Baker, D.(1970)Formation and interaction of ion-acoustic solitons, Phys. Rev. Lett. 25, 11-14 .
  • Ikezi, H.(1973)Experiments on ion-acoustic solitary waves, Phys. Fluids, 16, 1668-167.
  • Kato,Y., Tajiri, M. and Taniuti, T.(1972) Precursor of ion-acoustic quasishock wave in collisionless plasma, Phys. Fluids, 15, 865-870.
  • Taniuti, T.(1974) Reductive perturbation method and far fields of wave equations,Suppl. of Progress in Theoretical Phys., 55, 1-35.
  • N. Sugimoto and T. Kakutani, Note on the higher order terms in reductive perturbation theory, J. Phys. Soc. Japan, 43, 1469-1470 (1977).
  • Kodama, Y. and Taniuti, T.(1978) Higher order perturbation in the reductive perturbation method
  • I:Weakly dispersive systems, J. Phys. Soc. Japan, 45, 298-310. Malfliet, M. and Wieers, E.(1999) Theory of ion-acoustic waves re-visited, J. Plasma Phys., 56, 441
  • Demiray, H.(1999) A modified reductive perturbation method as applied to nonlinear ion-acoustic waves, J. Phys. Soc. Japan, 68, 1833-1837.
  • Demiray, H.(2012) Contribution of higher order terms in the nonlinear shallow water waves, TWMS J. Appl. Engr. Math., 2, 210-218.
  • Williams, G., Kourakis, I., Verheest, F. and Hellberg, M. A.(2013) Re-examining the Cairns-Tsallis model for ion acoustic solitons, Physical Review E, 88, 023103.
  • Hilmi Demiray, for a photograph and biography, see TWMS Journal of Applied and Engineering Mathematics, Volume 1, No.1, 2011.
There are 24 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

H. Demiray This is me

Publication Date December 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 2

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