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On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission line

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Abstract

This paper focuses on finding soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission lattice. Our investigation is based on the fact that for a realistic system, the electrical characteristics of a capacitor (and an inductor via skin effect) should include a fractional-order time derivative. In this respect for the model under consideration, we derive a fractional nonlinear partial differential equation for the voltage dynamics by applying the Kirchhoff’s laws. It is realized that the behavior of new soliton solutions obtained is influenced by the fractional-order time derivative as well as the coupling values. The fractional order also modifies the propagation velocity of the voltage wave notwithstanding their structure and tends to set up localized structure for low coupling parameter values. However, for a high value of the coupling parameter, the fractional order is less seen on the shapes of the new solitary solutions that are analytically derived. Several methods such as the Kudryashov method, the \((G'/G)\)-expansion method, the Jacobi elliptical functions method and the Weierstrass elliptic function expansion method led us to derive these solitary solutions while using the modified Riemann–Liouville derivatives in addition to the fractional complex transform. An insight into the overall dynamics of our network is provided through the analysis of the phase portraits.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their useful and valuable comments and suggestions.

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Authors and Affiliations

  1. Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teacher’s Training College, University of Yaoundé 1, P.O. Box 47, Yaoundé, Cameroon

    Emmanuel Fendzi-Donfack

  2. Pure Physics Laboratory, Group of Nonlinear Physics and Complex Systems, Department of Physics, Faculty of science, University of Douala, P.O. Box 24157, Douala, Cameroon

    Emmanuel Fendzi-Donfack, Jean Pierre Nguenang & Laurent Nana

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  1. Emmanuel Fendzi-Donfack
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Fendzi-Donfack, E., Nguenang, J.P. & Nana, L. On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission line. Nonlinear Dyn 104, 691–704 (2021). https://doi.org/10.1007/s11071-021-06300-x

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