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Dust ion acoustic bi-soliton, soliton, and shock waves in unmagnetized plasma with Kaniadakis-distributed electrons in planar and nonplanar geometry

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Abstract

This article presents bi-soliton, soliton, and shock solutions for the ion-acoustic wave (IAW) propagating in an unmagnetized nonplanar dusty plasma containing cold ions, neutral particles, and the electrons obeying \(\kappa \)-deformed Kaniadakis distribution. Applying the reductive perturbation method (RPM) to the basic equations, the nonplanar KdV–Burger (KdVB) equation is derived. It is found that there is a parametric domain for which the nonlinear coefficient vanishes, and naturally, the infinite divergence of the amplitude of the soliton arises. To describe the dynamic features of the wave quantities at or near the parametric domain, the nonplanar modified KdV–Burger (mKdVB) equation is constructed. The dissipation effect in the viscous plasma is expressed in the current study by a Burgers term, and the weighted residual method (WRM) is used to produce a solitary-type progressive wave solution for very small values of the Burgers term. Hirota’s bilinear formalism is employed for finding the multi-soliton solutions for the nonplanar mKdV system. However, the strong dissipation may cause the origination of a shock solution. An approximate analytical solution is also explored by means of WRM, through which the evolution of shock waves is determined. Finally, under the variation of various physical parameters, the evolution of different types of wave quantities is numerically examined.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: No data are used for this article.]

References

  1. R.Z. Sagdeev, Reviews of Plasma Physics, vol. 4 (Consultants Bureau, New York, 1966). (M A Leontovich)

    Google Scholar 

  2. H. Ikezi, R. Taylor, D. Baker, Phys. Rev. Lett. 44, 11 (1970)

    ADS  Google Scholar 

  3. R.E. Ergun, C.W. Carlson, J.P. McFadden, F.S. Mozer, G.T. Delory, W. Peria, C.C. Chaston, M. Temerin, I. Roth, L. Muschietti, R. Elphic, R. Strangeway, R. Pfaff, C.A. Cattell, D. Klumpar, E. Shelley, W. Peterson, E. Moebius, L. Kistler, Geophys. Res. Lett. 25(12), 2041–2044 (1998)

    ADS  Google Scholar 

  4. P. Schippers, M. Blanc, N. André, I. Dandouras, G.R. Lewis, L.K. Gilbert, A.M. Persoon, N. Krupp, D.A. Gurnett, A.J. Coates, S.M. Krimigis, Geophys. Res. Space Phys. 113 (A07208) (2008)

  5. S. Bansal, M. Aggarwal, T.S. Gill, Phys. Plasmas 27(8), 083704 (2020)

    ADS  Google Scholar 

  6. S. Raut, S. Roy, R.R. Kairi, P. Chatterjee, Int. J. Appl. Comput. Math. 7, 157 (2021)

    Google Scholar 

  7. S. Raut, K.K. Mondal, P. Chatterjee, A. Roy, Pramana J. Phys. 95, 73 (2021)

    ADS  Google Scholar 

  8. S. Roy, S. Saha, S. Raut, A.N. Das, J. Appl. Math. Comput. Mech. 20(2), 65–76 (2021)

    MathSciNet  Google Scholar 

  9. H.R. Miller, P.J. Witter, Active Galactic Nuclei (Springer, Berlin, 1987), p.202

    Google Scholar 

  10. A.V. Gurevich, Y. Istomin, Physics of the Pulsar Magnetosphere (Cambridge University Press, Cambridge, 1993)

    MATH  Google Scholar 

  11. F.C. Michel, Theory of pulsar magnetospheres. Rev. Mod. Phys. 54, 1–66 (1982)

    ADS  Google Scholar 

  12. E. Tandberg-Hansen, A.G. Emslie, The Physics of Solar Flares (Cambridge University Press, Cambridge, 1988)

    Google Scholar 

  13. P. Goldreich, W.H. Julian, Pulsar electrodynamics. Astrophys. J. 157, 869 (1969)

    ADS  Google Scholar 

  14. P.K. Shukla, V.P. Silin, Phys. Scr. 45, 508 (1992)

    ADS  Google Scholar 

  15. A. Barkan, N.D. Angelo, R.N. Merlino, Planet. Space Sci. 44, 239 (1996)

    ADS  Google Scholar 

  16. N. D’Angelo, J. Phys. D 28, 1009 (1995)

    ADS  Google Scholar 

  17. N. Dubouloz, R. Pottelette, M. Malingre, R.A. Treumann, Geophys. Res. Lett. 18(2), 155–158 (1991)

    ADS  Google Scholar 

  18. P.K. Shukla, A.A. Mamun, Bristol: IOP Publishing Ltd (2008)

  19. S. Sultana, G. Sarri, I. Kourakis, Phys. Plasmas 19(1), 012310 (2012)

    ADS  Google Scholar 

  20. Y.V. Bludov, V.V. Konotop, N. Akhmediev, Phys. Rev. E 80(3), 033610 (2009)

    ADS  Google Scholar 

  21. S.A. El-Tantawy, A.T. Elgendy, S. Ismail, Phys. Lett. A 381(40), 3465–3471 (2017)

    MathSciNet  ADS  Google Scholar 

  22. K. Watanabe, T. Taniuti, J. Phys. Soc. Jpn. 43(5), 1819–1820 (1977)

    ADS  Google Scholar 

  23. M.Y. Yu, P.K. Shukla, J. Plasma Phys. 29(3), 409–413 (1983)

    ADS  Google Scholar 

  24. R. Sarma, A.N. Dev, B. Boro, R. Das, N.C. Adhikary, Eur. Phys. J. D 74, 1–9 (2020)

    Google Scholar 

  25. G. Kaniadakis, Physica A 296, 405 (2001)

    ADS  Google Scholar 

  26. C. Beck, E.G.D. Cohen, Physica A 322, 267 (2003)

    MathSciNet  ADS  Google Scholar 

  27. K. Ourabah, L.A. Gougam, M. Tribeche, Phys. Rev. E 91, 012133 (2015)

    ADS  Google Scholar 

  28. T.S. Biro, G. Kaniadakis, Eur. Phys. J. B 50, 3 (2006)

    ADS  Google Scholar 

  29. K. Ourabah, A.H. Hamici-Bendimerad, M. Tribeche, Phys. Scr. 90, 045101 (2015)

    ADS  Google Scholar 

  30. K. Ourabah, M. Tribeche, Phys. Rev. E 89, 062130 (2014)

    ADS  Google Scholar 

  31. G. Kaniadakis, Phys. Rev. E 66, 056125 (2002)

    MathSciNet  ADS  Google Scholar 

  32. A.M. Teweldeberhan, H.G. Miller, G. Tegen, Int. J. Mod. Phys. E 12, 669 (2003)

    ADS  Google Scholar 

  33. S. Maxon, J. Viecelli, Cylindrical solitons. J. Phys. Fluids 17, 1614 (1974)

    ADS  Google Scholar 

  34. Y. Nishida, T. Nagasawa, S. Kawamata, Phys. Lett. 69, 196–198 (1978)

    Google Scholar 

  35. N. Hershkowitz, J. Glanz, K.E. Lonngren, Plasma Phys. 21(6), 583–588 (1979)

    ADS  Google Scholar 

  36. T. Chen, L. Schott, Phys. Lett. A 58(7), 459–461 (1976)

    ADS  Google Scholar 

  37. J.K. Xue, Phys. Lett. A 322(3–4), 225–230 (2004)

    ADS  Google Scholar 

  38. A.A. Mamun, P.K. Shukla, Phys. Lett. A 290(3–4), 173–175 (2001)

    ADS  Google Scholar 

  39. D.N. Gao, Z.R. Zhang, J.P. Wu, D. Luo, W.S. Duan, Z.Z. Li, Braz. J. Phys. 49, 693–697 (2019)

    ADS  Google Scholar 

  40. W. Masood, N. Imtiaz, M. Siddiq, Phys. Scr. 80(1), 015501 (2009)

    ADS  Google Scholar 

  41. S.A. Khan, S. Mahmood, S. Ali, Phys. Plasmas 16(4), 044505 (2009)

    ADS  Google Scholar 

  42. B. Sahu, M. Tribeche, Phys. Plasmas 19(2), 022304 (2012)

    ADS  Google Scholar 

  43. B. Sahu, R. Roychoudhury, Phys. Plasmas 10(10), 4162–4165 (2003)

    ADS  Google Scholar 

  44. H. Demiray, Chaos Solitons Fractals 130, 109448 (2020)

    MathSciNet  Google Scholar 

  45. A.R. Seadawy, Comput. Math. Appl. 67(1), 172–180 (2014)

    MathSciNet  Google Scholar 

  46. A.R. Seadawy, Appl. Math. Inform. Sci. 10(1), 209 (2016)

    Google Scholar 

  47. A.R. Seadawy, D. Kumar, K. Hosseini, F. Samadani, Results Phys. 9, 1631–1634 (2018)

    ADS  Google Scholar 

  48. I. Ali, A.R. Seadawy, S.T.R. Rizvi, M. Younis, K. Ali, Int. J. Mod. Phys. B 34(30), 2050283 (2020)

    ADS  Google Scholar 

  49. A.R. Seadawy, N. Cheemaa, Indian J. Phys. 94(1), 117–126 (2020)

    ADS  Google Scholar 

  50. S.T.R. Rizvi, A.R. Seadawy, F. Ashraf, M. Younis, H. Iqbal, D. Baleanu, Results Phys. 19, 103661 (2020)

    Google Scholar 

  51. J. Wang, K. Shehzad, A.R. Seadawy, M. Arshad, F. Asmat, J. Taibah Univ. Sci. 17(1), 2163872 (2023)

    Google Scholar 

  52. G. Mandal, K. Roy, A. Paul, A. Saha, P. Chatterjee, Z. Naturforsch A 70(9), 703–711 (2015)

    ADS  Google Scholar 

  53. S.A. El-Tantawy, Chaos Solitons Fractals 93, 162–168 (2016)

    MathSciNet  ADS  Google Scholar 

  54. M.G. Hafez, Braz. J. Phys. 49, 221–231 (2019)

    ADS  Google Scholar 

  55. M. Yousaf Khattak, W. Masood, R. Jahangir, M. Siddiq, Waves Rand. Comp. Med. 1–17 (2021)

  56. S. Singla, N.S. Saini, Results Phys. 22, 103898 (2021)

    Google Scholar 

  57. M.Y. Khattak, W. Masood, R. Jahangir, M. Siddiq, H.A. Alyousef, S.A. El-Tantawy, Chaos Solitons Fractals 161, 112265 (2022)

    Google Scholar 

  58. M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, 1991)

    MATH  Google Scholar 

  59. V.B. Matveev, M.A. Salle, Darboux Transformations and Solitons (Springer, Berlin, 1991)

    MATH  Google Scholar 

  60. R. Hirota, The Direct Method in Soliton Theory (No. 155) (Cambridge University Press, Cambridge, 2004)

  61. N.A. El-Bedwehy, W.M. Moslem, Astrophys. Space Sci. 335(2), 435–442 (2011)

    ADS  Google Scholar 

  62. S.A. El-Tantawy, Astrophys. Space Sci. 361, 1–9 (2016)

    Google Scholar 

  63. K.K. Mondal, A. Roy, P. Chatterjee, S. Raut, Int. J. Appl. Comput. Math. 6, 1–17 (2020)

  64. S. Raut, K.K. Mondal, P. Chatterjee, A. Roy, SeMA 78, 1–23 (2021)

    MathSciNet  Google Scholar 

  65. S. Roy, R.R. Kairi, S. Raut, Braz. J. Phys. 51(6), 1651–1660 (2021)

    ADS  Google Scholar 

  66. S. Roy, S. Raut, R.R. Kairi, Pramana 96(2), 67 (2022)

    ADS  Google Scholar 

  67. H. Demiray, C. Bayındır, Phys. Plasmas 22(9), 092105 (2015)

    ADS  Google Scholar 

  68. H. Demiray, E.R. El-Zahar, Phys. Plasmas 25(4), 042102 (2018)

    ADS  Google Scholar 

  69. H. Demiray, E.R. El-Zahar, Results Phys. 18, 103293 (2020)

    Google Scholar 

  70. G. Kaniadakis, Phys. Rev. E 66(5), 056125 (2002)

    MathSciNet  ADS  Google Scholar 

  71. T. Taniuti, Suppl. Progress Theor. Phys. 55, 1–35 (1974)

    ADS  Google Scholar 

  72. S. Raut, S. Roy, S. Saha, A.N. Das, Int. J. Appl. Comput. Math. 8(4), 196 (2022)

    Google Scholar 

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Acknowledgements

The authors are appreciative of the reviewers for insightful criticism and recommendations, which allowed us to raise the standard of the paper. Mr. Subrata Roy (JRF) gratefully acknowledges the research Fellowship received from University Grants Commission (UGC)[No. 1106/2018].

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Author notes

  1. Santanu Raut, Kajal Kumar Mondal and Prasanta Chatterjee have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Mathabhanga College, Cooch Behar, West Bengal, 736164, India

    Santanu Raut

  2. Department of Mathematics, Cooch Behar Panchanan Barma University, Cooch Behar, 736101, India

    Kajal Kumar Mondal & Subrata Roy

  3. Siksha Bhavana, Visva-Bharati, Santiniketan, 731235, India

    Prasanta Chatterjee

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  1. Santanu Raut
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Correspondence to Subrata Roy.

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Raut, S., Mondal, K.K., Chatterjee, P. et al. Dust ion acoustic bi-soliton, soliton, and shock waves in unmagnetized plasma with Kaniadakis-distributed electrons in planar and nonplanar geometry. Eur. Phys. J. D 77, 100 (2023). https://doi.org/10.1140/epjd/s10053-023-00676-8

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