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Some new families of solitary wave solutions of the generalized Schamel equation and their applications in plasma physics

  • Nadia Cheemaa
  • Aly R. SeadawyEmail author
  • Sheng Chen
Regular Article

Abstract.

In this article we studied analytically the propagation of nonlinear ion acoustic solitary waves modeled by the generalized Schamel (GS) equation arising in plasma physics using auxiliary equation mapping method. As a result, we found a series of more general and new families of solutions, which are more powerful in the development of soliton dynamics, quantum plasma, adiabatic parameter dynamics, biomedical problems, fluid dynamics, industrial studies and many other fields. The calculations prove that this method is more reliable, straightforward, and effective to study analytically other nonlinear complicated physical problems modeled by complex nonlinear partial differential equations arising in mathematical physics, hydrodynamics, fluid mechanics, mathematical biology, plasma physics, engineering disciplines, chemistry and many other natural sciences. We also have expressed our solutions graphically with the help of Mathematica 10.4 to understand physically the behavior of different shapes of ion acoustic solitary waves including kink-type, anti-kink-type, half-bright and dark soliton.

References

  1. 1.
    C.S. Gardener, J.M. Green, M.D. Kruskal, R.M. Miura, Phys. Rev. Lett. 19, 1095 (1967)ADSCrossRefGoogle Scholar
  2. 2.
    H. Schamel, Plasma Phys. 14, 905 (1972)ADSCrossRefGoogle Scholar
  3. 3.
    H. Schamel, J. Plasma Phys. 9, 377 (1973)ADSCrossRefGoogle Scholar
  4. 4.
    Z. Horii, Phys. Lett. A 306, 45 (2002)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    L.P. Zhang, J.K. Xue, Chaos, Solitons Fractals 23, 543 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    R.M. EL-Shiekh, Math. Methods Appl. Sci. 36, 1 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    A.H. Khater, M.M. Hassan, R.S. Temsah, Math. Comput. Simul. 70, 221 (2005)CrossRefGoogle Scholar
  8. 8.
    Aly R. Seadawy, Physica A 439, 124 (2015)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Aly Seadawy, Eur. Phys. J. Plus 132, 518 (2017)CrossRefGoogle Scholar
  10. 10.
    Aly R. Seadawy, D. Lu, Results Phys. 6, 590 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    Aly R. Seadawy, Physica A 455, 44 (2016)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Aly R. Seadawy, Sultan Z. Alamri, Results Phys. 8, 286 (2018)ADSCrossRefGoogle Scholar
  13. 13.
    A.R. Seadawy, K. El-Rashidy, Math. Comput. Model. 57, 13 (2013)CrossRefGoogle Scholar
  14. 14.
    A.R. Seadawy, Appl. Math. Lett. 25, 687 (2012)MathSciNetCrossRefGoogle Scholar
  15. 15.
    M. Arshad, A.R. Seadawy, D. Lu, J. Wang, Chin. J. Phys. 55, 780 (2017)CrossRefGoogle Scholar
  16. 16.
    M. Arshad, Aly R. Seadawy, Dianchen Lu, Optik 138, 40 (2017)ADSCrossRefGoogle Scholar
  17. 17.
    Asghar Ali, A.R. Seadawya, Dianchen Lu, Optik 145, 79 (2017)ADSCrossRefGoogle Scholar
  18. 18.
    Dianchen Lu, A.R. Seadawy, M. Arshad, Jun Wang, Results Phys. 7, 899 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    M. Arshad, A.R. Seadawy, Dianchen Lu, Jun Wang, Results Phys. 6, 1136 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    S.A.R. Horsley, J. Opt. 18, 085104 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    S.A.R. Horsley, Am. J. Phys. 85, 439 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    S.A.R. Horsley, C.G. King, T.G. Philbin, J. Opt. 18, 044016 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    Xiao-Jun Yang, Appl. Math. Lett. 64, 193 (2017)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Xiao-Jun Yang, Feng Gao, H.M. Srivastava, J. Comput. Appl. Math. 339, 285 (2018)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Xiao-Jun Yang, Feng Gao, H.M. Srivastava, Comput. Math. Appl. 73, 203 (2017)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Xiao-Jun Yang, J.A. Tenreiro Machado, Dumitru Baleanu, Fractals 25, 1740006 (2017)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Yingxin Guo, Dyn. Syst. 32, 490 (2017)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Lin Gao, Chengzheng Cai, Peng Hou, Therm. Sci. 21, 71 (2017)CrossRefGoogle Scholar
  29. 29.
    Xiao-Jun Yang, Feng Gao, Therm. Sci. 21, 133 (2017)CrossRefGoogle Scholar
  30. 30.
    M.A. Helal, A.R. Seadawy, Phys. Scr. 80, 350 (2009)CrossRefGoogle Scholar
  31. 31.
    A.H. Khater, D.K. Callebaut, A.R. Seadawy, Phys. Scr. 62, 353 (2000)ADSCrossRefGoogle Scholar
  32. 32.
    A.H. Khater, D.K. Callebaut, M.A. Helal, A.R. Seadawy, Eur. Phys. J. D 39, 237 (2006)ADSCrossRefGoogle Scholar
  33. 33.
    Aly R. Seadawy, Int. J. Comput. Methods 15, 1850017 (2018)MathSciNetCrossRefGoogle Scholar
  34. 34.
    A.R. Seadawy, Eur. Phys. J. Plus 130, 182 (2015)CrossRefGoogle Scholar
  35. 35.
    D. Lu, A.R. Seadawy, M. Iqbal, Results Phys. 11, 1161 (2018)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Nejoh, J. Phys. A 23, 1973 (1990)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    G.C. Das, k.M. Sen, Contrib. Plasma Phys. 31, 647 (1991)ADSCrossRefGoogle Scholar
  38. 38.
    G.C. Das, k.M. Sen, Planet. Space Sci. 42, 41 (1994)ADSCrossRefGoogle Scholar
  39. 39.
    F. Verheet, W. Hereman, Phys. Scr. 50, 611 (1994)ADSCrossRefGoogle Scholar
  40. 40.
    F. Kangalgil, J. Egypt. Math. Soc. 24, 526 (2016)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Aly R. Seadawy, Math. Methods Appl. Sci. 40, 1598 (2017)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    W.M. Taha, M.S.M. Noorani, I. Hashim, J. Appl. Math. 2013, 810729 (2013)CrossRefGoogle Scholar
  43. 43.
    J. Lee, R. Sakthivel, Rep. Math. Phys. 68, 153 (2011)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    N.O. Al Atawi, J. Math. Res. 9, 5 (2017)CrossRefGoogle Scholar
  45. 45.
    F. Awawdeh, H.M. Jaradat, S. Al-Shara, Eur. Phys. J. D 66, 40 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    A.H. Khater, M.M. Hassan, Exact solutions expressible in hyperbolic and Jacobi elliptic functions of some important equations of ion-acoustic waves, in Acoustic Waves - From Microdevices to Helioseismology (2011) pp. 67--78Google Scholar
  47. 47.
    J. Yang, S. Tang, J. Math. Sci. 31, 25 (2015)Google Scholar
  48. 48.
    M. Iqbal, A.R. Seadawy, D. Lu, Mod. Phys. Lett. A 33, 1850217 (2018)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Mathematics, Faculty of ScienceTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia
  3. 3.Mathematics Department, Faculty of ScienceBeni-Suef UniversityBeni SuefEgypt

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