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Competent closed form soliton solutions to the nonlinear transmission and the low-pass electrical transmission lines

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Abstract

The nonlinear transmission line and the low-pass electrical transmission line equations are very important nonlinear evolution equations in electrical transmission line management. The modified simple equation (MSE) technique is a compatible and effective mathematical tool to extract soliton solutions of science and engineering problems. In this article, the MSE technique is introduced and implemented to extract broad-ranging exact wave solutions to the formerly stated equations and accomplish analytic soliton solutions including trigonometric and hyperbolic functions with parameters. Whenever the parameters accept appropriate values, soliton solutions are formulated from the wave solutions. We describe the solutions through 3D and 2D graphs. The shapes of the obtained solutions include kink soliton, peakon, periodic soliton, singular periodic soliton, bell shape soliton, compacton and singular kink type soliton. The results show that the MSE technique is a further operative and powerful mathematical tool for extracting the soliton solutions.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

    Md. Abdul Kayum & M. Ali Akbar

  2. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    M. S. Osman

  3. Department of Mathematics, Faculty of Applied Science, Umm Alqura University, Mecca, 21955, Saudi Arabia

    M. S. Osman

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  1. Md. Abdul Kayum
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  2. M. Ali Akbar
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  3. M. S. Osman
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Correspondence to M. S. Osman.

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Kayum, M.A., Akbar, M.A. & Osman, M.S. Competent closed form soliton solutions to the nonlinear transmission and the low-pass electrical transmission lines. Eur. Phys. J. Plus 135, 575 (2020). https://doi.org/10.1140/epjp/s13360-020-00573-8

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