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Cylindrical and Spherical Ion-Acoustic Shock and Solitary Waves in a Nonplanar Hybrid q-nonextensive Nonthermal Plasma

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Nonlinear Dynamics and Applications

Abstract

In this article we investigate the propagating properties of ion-acoustic wave (IAW) in a plasma comprising positively charged ions and electrons abiding by hybrid q-non-extensive non-thermal velocity distribution equation. The nonplanar KdV-Burger (NKDVB) equation is derived from the basic governing equation. Considering the impact from the ion streaming velocity, inter-particle collisions, and viscosity, a Burgers term is introduced in the present system and using Weighted Residual Method (WRM) and Simplified Hirota bilinear method (SHBM) progressive solitary wave solution and shock wave are derived. Finally, the effect of different physical parameters on solitary and shock wave on the propagation of IAW in the present plasma environment is noticed.

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References

  1. Sagdeev, R.Z.: Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23 (1966)

    Google Scholar 

  2. Taylor, R.J., Baker, D.R., Ikezi, H.: Observation of collisionless electrostatic shocks. Phys. Rev. Lett. 24(5), 206 (1970)

    Google Scholar 

  3. Shukla, P.K., Silin, V.P.: Dust ion-acoustic wave. Phys. Scr. 45(5), 508 (1992)

    Google Scholar 

  4. Barkan, A., D’angelo, N., Merlino, R.L.: Experiments on ion-acoustic waves in dusty plasmas. Planet. Space Sci. 44(3), 239–242 (1996)

    Google Scholar 

  5. D’Angelo, N.: Coulomb solids and low-frequency fluctuations in RF dusty plasmas. J. Phys. D: Appl. Phys. 28(5), 1009 (1995)

    Google Scholar 

  6. Dubouloz, N., Pottelette, R., Malingre, M., Treumann, R.A.: Generation of broadband electrostatic noise by electron acoustic solitons. Geophys. Res. Lett. 18(2), 155–158 (1991)

    Google Scholar 

  7. Maxon, S., Viecelli, J.: Cylindrical solitons. Phys. Fluids 17(8), 1614–1616 (1974)

    Google Scholar 

  8. Gao, D.N., Zhang, Z.R., Wu, J.P., Luo, D., Duan, W.S., Li, Z.Z.: Cylindrical and Spherical Dust-Ion Acoustic Solitary Waves by Damped Korteweg-de Vries-Burgers Equation. Braz. J. Phys. 49(5), 693–697 (2019)

    Google Scholar 

  9. Masood, W., Imtiaz, N., Siddiq, M.: Ion acoustic shock waves in dissipative electron-positron-ion plasmas with weak transverse perturbations. Phys. Scr. 80(1), 015501 (2009)

    Google Scholar 

  10. Roy, S., Saha, S., Raut, S., Das, A.N.: Studies on the effect of kinematic viscosity on electron-acoustic cylindrical and spherical solitary waves in a plasma with trapped electrons. J. Appl. Math. Comput. Mech. 20(2) (2021)

    Google Scholar 

  11. Demiray, H.: Analytical solution for nonplanar waves in a plasma with q-nonextensive nonthermal velocity distribution: weighted residual method. Chaos, Solitons & Fractals 130, 109448 (2020)

    Google Scholar 

  12. Raut, S., Mondal, K.K., Chatterjee, P., Roy, A.: Propagation of dust-ion-acoustic solitary waves for damped modified Kadomtsev-Petviashvili-Burgers equation in dusty plasma with a q-nonextensive nonthermal electron velocity distribution. SeMA J. 1–23 ( 2021)

    Google Scholar 

  13. Williams, G., Kourakis, I., Verheest, F., Hellberg, M.A.: Re-examining the Cairns-Tsallis model for ion acoustic solitons. Phys. Rev. E 88(2), 023103 (2013)

    Google Scholar 

  14. Cairns, R.A., Bingham, R., Dendy, R.O., Nairn, C.M.C., Shukla, P.K., Mamun, A.A.: Ion sound solitary waves with density depressions. Le J. de Phys. IV 5(C6), C6-43, 072306 (1995)

    Google Scholar 

  15. Taniuti, T.: Reductive perturbation method and far fields of wave equations. Prog. Theor. Phys. Suppl. 55, 1–35, 023103 (1974)

    Google Scholar 

  16. Mushtaq, A., Shah, H.A.: Nonlinear Zakharov-Kuznetsov equation for obliquely propagating two-dimensional ion-acoustic solitary waves in a relativistic, rotating magnetized electron-positron-ion plasma. Phys. Plasmas 12(7), 072306 (2005)

    Google Scholar 

  17. Awawdeh, F., Jaradat, H.M., Al-Shara, S.: Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma. Eur. Phys. J. D 66(2), 1–8, 072306 (2012)

    Google Scholar 

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Correspondence to Subrata Roy .

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Roy, S., Raut, S., Kairi, R.R. (2022). Cylindrical and Spherical Ion-Acoustic Shock and Solitary Waves in a Nonplanar Hybrid q-nonextensive Nonthermal Plasma. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_11

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