zbMATH — the first resource for mathematics

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.

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q51 Soliton equations
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.