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Traveling and localized solitary wave solutions of the nonlinear electrical transmission line model equation

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Abstract

Analytical solutions describing the kink–antikink type, hyperbolic, trigonometric, doubly periodic, localized bright and dark soliton like, breather and rational periodic train solutions to the discrete nonlinear electrical transmission line in \((2+1)\)-dimensions have been investigated with the Kudryashov method, the fractional linear transform method, and the simplest equation method with its modified and extended versions. Consequently, many new and more general explicit forms of traveling waves are retrieved under parametric conditions. The 3D, 2D, and density profile of some of the obtained results are numerically simulated by selecting suitable values of the various parameters of the NLTL model equation. Furthermore, all the obtained results were checked and verified by putting back into the considered nonlinear transmission line model equation with Maple and Mathematica software. The acquired results show the validity and reliability of the proposed schemes to the studied nonlinear electrical transmission line model.

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References

  1. L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers (Birkhauser, Boston, 1997)

    Book  Google Scholar 

  2. M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform (Cambridge Univ Press, Cambridge, 1990)

    MATH  Google Scholar 

  3. R. Hirota, The Direct Method in Soliton Theory (Cambridge University Press, Cambridge, 2004)

    Book  Google Scholar 

  4. M.A. Kayum, M.A. Akbar, M.S. Osman, Eur. Phys. J. Plus 135, 575 (2020)

    Article  Google Scholar 

  5. B.H. Malwe, G. Betchewe, S.Y. Doka, T.C. Kofane, Nonlinear Dyn. 84, 171 (2016)

    Article  Google Scholar 

  6. T.S. Raju, P.K. Panigrahi, K. Porsezian, Phys. Rev. E 72, 046612 (2005)

    Article  ADS  Google Scholar 

  7. M.M. El-Borai, H.M. El-Owaidy, H.M. Ahmed, A.H. Arnous, Nonlinear Dyn. 87, 767 (2017)

    Article  Google Scholar 

  8. A. Biswas, H. Rezazadeh, M. Mirzazadeh, M. Eslami, Q. Zhou, S.P. Moshokoa, M. Belic, Optik 164, 380 (2018)

    Article  ADS  Google Scholar 

  9. A.J. Mohamad Jawad, A. Biswas, Q. Zhou, S.P. Moshokoa, M. Belic, Optik 165, 111 (2018)

  10. A. Biswas, Y. Yildirim, E. Yasar, Q. Zhou, S.P. Moshokoa, M. Belic, Optik 160, 24 (2018)

    Article  ADS  Google Scholar 

  11. H. Kumar, F. Chand, J. Theor. Appl. Phys. 8, 114 (2014)

    Article  ADS  Google Scholar 

  12. E.M.E. Zayed, K.A.E. Alurrfi, Chaos Solitons Fractal 78, 148 (2015)

    Article  ADS  Google Scholar 

  13. H. Kumar, F. Chand, Opt. Laser Technol. 54, 265 (2013)

    Article  ADS  Google Scholar 

  14. A. Malik, H. Kumar, R.P. Chahal, F. Chand, Pramana J. Phys. 92, 8 (2019)

  15. M.T. Gulluoglu, Open Phys. 17, 823 (2019)

    Article  Google Scholar 

  16. A.M. Shahoot, K.A.E. Alurrfi, M.O.M. Elmrid, A.M. Almsiri, A.M.H. Arwiniya, J. Taibah Univ. Sci. 13, 63 (2019)

    Article  Google Scholar 

  17. E. Fendzi-Donfack, J.P. Nguenang, L. Nana, Eur. Phys. J. Plus 133, 32 (2018)

    Article  Google Scholar 

  18. G.R. Deffo, S.B. Yamgoue, F.B. Pelap, Eur. Phys. J. B 91, 242 (2018)

    Article  ADS  Google Scholar 

  19. M.O. Al-Amr, Comput. Math. Appl. 69, 390 (2015)

    Article  MathSciNet  Google Scholar 

  20. M.B. Hubert, G. Betchewe, S.Y. Doka, K.T. Crepin, Appl. Math. Comput. 239, 299 (2014)

    MathSciNet  Google Scholar 

  21. M.O. Al-Amr, S. El-Ganaini, Comput. Math. Appl. 74, 1274 (2017)

    Article  MathSciNet  Google Scholar 

  22. A. Malik, F. Chand, H. Kumar, S.C. Mishra, Comput. Math. Appl. 64, 2850 (2012)

    Article  MathSciNet  Google Scholar 

  23. E. Tala-Tebue, D.C. Tsobgni-Fozap, A. Kenfack-Jiotsa, T.C. Kofane, Eur. Phys. J. Plus 129, 136 (2014)

    Article  Google Scholar 

  24. N.K. Vitanov, Commun. Nonlinear Sci. Numer. Simul. 15, 2050 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  25. N.K. Vitanov, Commun. Nonlinear Sci. Numer. Simul. 16, 1176 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  26. N.A. Kudryashov, Commun. Nonlinear Sci. Numer. Simul. 17, 2248 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  27. E.M.E. Zayed, S.A.H. Ibrahim, Chin. Phys. Lett. 29, 060201 (2012)

    Article  Google Scholar 

  28. S. El-Ganaini, H. Kumar, Chaos Solitons Fractal 140, 110218 (2020)

    Article  ADS  Google Scholar 

  29. N.A. Kudryashov, Chaos Solitons Fractal 24, 1217 (2005)

    Article  ADS  Google Scholar 

  30. N.A. Kudryashov, Phys. Lett. A 342, 99 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  31. N.A. Kudryashov, Commun. Nonlinear Sci. Numer. Simul. 17, 2248 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  32. S. Bilige, T. Chaolu, Appl. Math. Comput. 216, 3146 (2010)

    MathSciNet  Google Scholar 

  33. S. Bilige, T. Chaolu, X. Wang, Appl. Math. Comput. 224, 517 (2013)

    MathSciNet  Google Scholar 

  34. P. Marquié, J.M. Bilbault, M. Remoissenet, Phys. Rev. E 49, 828 (1994)

    Article  ADS  Google Scholar 

  35. R. Hirota, K. Suzuki, Proc. IEEE 61, 1483 (1973)

    Article  Google Scholar 

  36. T. Yoshinaga, T. Kakutani, J. Phys. Soc. Jpn. 49, 2072 (1980)

  37. T. Kakutani, N. Yamasaki, J. Phys. Soc. Jpn. 45, 674 (1978)

    Article  ADS  Google Scholar 

  38. D. Yemélé, T.C. Kofané, J. Phys. D 39, 4504 (2006)

    Article  ADS  Google Scholar 

  39. D.C. Hutchings, J.M. Arnold, J. Opt. Soc. Am. B 16, 513 (1999)

    Article  ADS  Google Scholar 

  40. S.I. Mostafa, Chaos Solitons Fractals 39, 2125 (2009)

    Article  ADS  Google Scholar 

  41. P. Marquié, J.M. Bilbault, M. Remoissenet, Phys. Rev. E 51, 612 (1995)

    Article  ADS  Google Scholar 

  42. E. Tala-Tebue, E.M.E. Zayed, Eur. Phys. J. Plus 133, 314 (2018)

    Article  Google Scholar 

  43. M.A. Kayum, S. Ara, H.K. Barman, M.A. Akbar, Results Phys. 18, 103269 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to thank the anonymous referees for their valuable comments.

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Authors and Affiliations

  1. Department of Physics, Pt. Neki Ram Sharma Government College, Rohtak, Haryana, 124001, India

    Hitender Kumar

  2. Faculty of Science, Department of Mathematics, Damanhour University, Bahira, 22514, Egypt

    Shoukry El-Ganaini

Authors
  1. Hitender Kumar
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  2. Shoukry El-Ganaini
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Correspondence to Hitender Kumar.

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Kumar, H., El-Ganaini, S. Traveling and localized solitary wave solutions of the nonlinear electrical transmission line model equation. Eur. Phys. J. Plus 135, 749 (2020). https://doi.org/10.1140/epjp/s13360-020-00750-9

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00750-9

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