| Citation: |
Yan Zhou, Jie Song, Tong Han. SOLITARY WAVES, PERIODIC PEAKONS, PSEUDO-PEAKONS AND COMPACTONS GIVEN BY THREE ION-ACOUSTIC WAVE MODELS IN ELECTRON PLASMAS[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 810-828. doi: 10.11948/2156-907X.20190028
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SOLITARY WAVES, PERIODIC PEAKONS, PSEUDO-PEAKONS AND COMPACTONS GIVEN BY THREE ION-ACOUSTIC WAVE MODELS IN ELECTRON PLASMAS
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Abstract
The nonlinear ion-acoustic oscillations models are governed by three partial differential equation systems. Their travelling wave equations are three first class singular traveling wave systems depending on different parameter groups, respectively. By using the method of dynamical system and the theory of singular traveling wave systems, in this paper, it is shown that there exist parameter groups such that these singular systems have solitary wave solutions, pseudo-peakons, periodic peakons and compactons as well as kink and anti-kink wave solutions. The results of this paper complete the studies of three papers [5, 13] and [14]. -
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References
[1] G. C. Das, Rotation as a progenitor of various solitary waves in magnetized plasmas, Chaos Solit. Fract., 2017, 101, 33-40. doi: 10.1016/j.chaos.2017.05.007 [2] S. Ghebache, M. Tribeche, Nonlinear ion-acoustic double-layers in electronegative plasmas with electrons featuring Tsallis distribution, Physica A, 2016, 447, 180-187. doi: 10.1016/j.physa.2015.12.026 [3] S. Ghebache, M. Tribeche, Arbitrary amplitude ion-acoustic solitary waves in electronegative plasmas with electrons featuring Tsallis distribution, Physica A, 2017, 483, 193-200. doi: 10.1016/j.physa.2017.04.183 [4] W. F. El Taibany, M. Tribeche, Nonlinear ion-acoustic solitary waves in electronegative plasmas with electrons featuring Tsallis distribution, Phys. Plasmas, 2012, 19, 024507. doi: 10.1063/1.3684232 [5] M. M. Hatami, M. Tribeche, Arbitrary amplitude ion-acoustic solitary waves in a two-temperature nonextensive electron plasma, Physica A, 2018, 491, 55-63. doi: 10.1016/j.physa.2017.09.004 [6] J. Li, G. Chen, Bifurcations of travelling wave solutions for four classes of nonlinear wave equations, 2005, 15(12), 3973-3998. [7] J. Li, G. Chen, On a class of singular nonlinear traveling wave equations, Int. J. Bifurcation and Chaos, 2007, 17, 4049-4065. doi: 10.1142/S0218127407019858 [8] J. Li, Singular Nonlinear Traveling Wave Equations: Bifurcations and Exact Solutions, Science Press, Beijing, 2013. [9] J. Li, W. Zhou, G. Chen, Understanding peakons, periodic peakons and compactons via a shallow water wave equation, Int. J. Bifurcation and Chaos, 2016, 26(12), 1650207. doi: 10.1142/S0218127416502072 [10] J. Li, Periodic peakons, pseudo-peakons and compactons of ion-acoustic wave model in electronegative plasmas with electrons featuring tsallis distribution, Int. J. of Bifurcation and Chaos, 2018, 28(1), 1850015. doi: 10.1142/S0218127418500153 [11] J. Li, Solitary waves, periodic peakons and pseudo-peakons of the nonlinear acoustic wave model in rotating magnetized plasma, Int. J. of Bifurcation and Chaos, 2018, 28(4), 1850054. doi: 10.1142/S0218127418500542 [12] J. Li, Geometric properties and exact travelling wave solutions for the generalized Burger-Fisher equation and the Sharma-Tasso-Olver equation, J. of Nonlinear Modeling and Analysis, 2019, 1(1), 1-10. [13] O. R. Rufai, R. Bharuthram, Obliquely propagating low-frequency magnetospheric electrostatic solitary waves in the presence of an oxygen-ion beam, Commun Nonlinear Sci. Numer. Simulat., 2019, 68, 160-168. doi: 10.1016/j.cnsns.2018.08.006 [14] S. Sultana1, R. Schlickeiser, Fully nonlinear heavy ion-acoustic solitary waves in astrophysical degenerate relativistic quantum plasmas, Astrophys Space Sci., 2018, 363, 103. doi: 10.1007/s10509-018-3317-y [15] R. Z. Sagdeev, Reviews of Plasma Physics, in: M. A. Leontovich (Ed. ), Consultants Bureau, New York, 1966. -
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Yan Zhou, Jie Song, Tong Han. SOLITARY WAVES, PERIODIC PEAKONS, PSEUDO-PEAKONS AND COMPACTONS GIVEN BY THREE ION-ACOUSTIC WAVE MODELS IN ELECTRON PLASMAS[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 810-828. doi: 10.11948/2156-907X.20190028
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Figure 1. The graphs of function
$ Q_1(\phi) $ as$ M $ is varied. Parameter values:$ \beta = 0.1, \delta = 0.25, q_c = 0.5, q_h = 0.75, \sigma = 0.2; M_b = 2.133217589. $ -
Figure 2. The bifurcations of phase portraits of system (1.5) as
$ M $ is varied. Parameter values:$ \beta = 0.1, \delta = 0.25, q_c = 0.5, q_h = 0.75, \sigma = 0.2; M_b = 2.133217589. $ - Figure 4. The wave profiles of system (1.5) corresponding to the orbits in Fig.2 (g)
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Figure 3. The bifurcations of phase portraits of system (1.5) as
$ \beta $ is varied. Parameter values:$ \delta = 0.18, q_c = 0.16, q_h = 0.75, M = 2.15, \sigma = 0.12; \beta_b = 0.1814691367, \beta_k = 0.17199909 $ -
Figure 5. The bifurcations of phase portraits of system (1.13) as
$ M $ is varied. Parameter values:$ \alpha = 1.1, \gamma_i = 5/3, \gamma_e = 4/3, K_1 = 2, K_2 = 3; \beta_1 = \frac52, \beta_2 = 4; M_b = 1.081476141 $ - Figure 6. The different wave profiles of system (1.13)
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Figure 7. The graphs of function
$ Q_3(\psi) $ of system (1.21) as$ M $ is varied -
Figure 8. The bifurcations of phase portraits of system (1.21) as M is varied. Parameter values:
${\alpha _p} = 0.1,\gamma = \cos \frac{\pi }{4},p = 0.75,{v_0} = 0.2$ . In this case, Mcusp = 0.7462797351, Minf = 0.9968202790 - Figure 9. The wave profiles of system (1.14) corresponding to the orbits in Fig.8 (a)
- Figure 10. The wave profiles of system (1.14) corresponding to the orbits in Fig.F8 (f)