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New exact solitary wave solutions of the Zakharov-Kuznetsov equation in the electron-positron-ion plasmas. (English) Zbl 1441.76144
Summary: In this paper, the Zakharov-Kuznetsov equation which describes the propagation of the electrostatic excitations in the electron – positron – ion (e – p – i) plasmas is investigated. New exact solitary wave solutions are obtained using Hirota’s bilinear method and generalized three-wave approach. These new exact solutions will enrich previous results and help us further to understand the physical structures and analyze the dynamics of the electrostatic solitons in the e – p – i plasmas. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by phase velocity, ion-to-electron density ratio, rotation frequency and cyclotron frequency.

MSC:
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q51 Soliton equations
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[1] Dai, Z.; Lin, S.; Fu, H.; Zeng, X., Exact three-wave solutions for the KP equation, Appl. math. comput., 216, (2010)
[2] Gibbons, G.W.; Hawking, S.W.; Siklos, S., The very early universe, (1983), Cambridge University Press Cambridge
[3] He, J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos solitons fract., 26, 695-700, (2005) · Zbl 1072.35502
[4] Hirota, R., Direct methods in soliton theory, () · Zbl 0124.21603
[5] Hirota, R., Exact solutions of the korteweg – de Vries equation for multiple collisions of solitons, Phys. rev. lett., 27, 1192-1194, (1971) · Zbl 1168.35423
[6] Infeld, E.; Fryczs, P., Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas. part 2. numerical simulations, two-soliton collisions, J. plasma phys., 37, 97-106, (1987)
[7] Kourakis, I.; Moslem, W.M.; Abdelsalam, U.M.; Sabry, R.; Shukla, P.K., Nonlinear dynamics of rotating multi-component pair plasmas and e – p-i plasmas, Plasma fusion res., 4, 1-11, (2009)
[8] Kourakis, I.; Verheest, F.; Cramer, N., Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron – positron – ion plasmas, Phys. plasmas, 14, 022306, (2007)
[9] Moslem, W.M.; Ali, S.; Shukla, P.K.; Tang, X.Y.; Rowlands, G., Phys. plasmas, 14, 082308, (2007)
[10] Miller, H.R.; Witta, P.J., Active galactic nuclei, (1987), Springer-Verlag Berlin
[11] Qu, Q.; Tian, B.; Liu, W.; Sun, K.; Wang, P.; Jiang, Y.; Qin, B., Soliton solutions and interactions of the zakharov – kuznetsov equation in the electron – positron – ion plasmas, D eur. phys. J. D, 61, 709-715, (2011)
[12] Ruderman, M.A.; Sutherland, P.G., Theory of pulsars – polar caps, sparks, and coherent microwave radiation, Astrophys. J., 196, 51-72, (1975)
[13] Sahu, B.; Roychoudhury, R., Quantum ion acoustic shock waves in planar and nonplanar geometry, Phys. plasmas, 14, 072310, (2007)
[14] Shkula, P.K.; Mamun, A.A.; Stenflo, L., Vortices in a strongly magnetized electron – positron – ion plasma, Phys. scr., 68, 295-298, (2003) · Zbl 1129.76386
[15] Sturrock, P.A., A model of pulsars, Astrophys. J., 164, 529-556, (1971)
[16] Zakharov, V.E.; Kuznetsov, E.A., Three-dimensional solitons, Sov. phys., 39, 285-286, (1974)
[17] Zhang, B.; Liu, Z.; Xiao, Q., New exact solitary wave and multiple soliton solutions of quantum zakharov – kuznetsov equation, Appl. math. comput., 217, (2010) · Zbl 1200.35238
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