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Kink-soliton, singular-kink-soliton and singular-periodic solutions for a new two-mode version of the Burger–Huxley model: applications in nerve fibers and liquid crystals

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Abstract

New two-mode version of the generalized Burger–Huxley equation is derived using Korsunsky’s operators. The new model arises in the applications of nerve fibers and liquid crystals, and it describes the interaction of two symmetric waves moving simultaneously in the same direction. Solitary wave solutions of types kink-soliton, singular-kink-soliton and singular-periodic are obtained to this model by means of the simplified bilinear method, polynomial-function method and the Kudryashov-expansion method. A comprehensive graphical analysis is conducted to show some physical properties of this new type of nonlinear equations. Finally, all obtained solutions are verified by direct substitutions in the new model.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Jordan University of Science & Technology, Irbid, 22110, Jordan

    Marwan Alquran

  2. Department of Computer Engineering, Biruni University, Istanbul, Turkey

    Tukur Abdulkadir Sulaiman & Abdullahi Yusuf

  3. Department of Mathematics, Federal University Dutse, Jigawa, Nigeria

    Tukur Abdulkadir Sulaiman & Abdullahi Yusuf

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  1. Marwan Alquran
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  2. Tukur Abdulkadir Sulaiman
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  3. Abdullahi Yusuf
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Correspondence to Abdullahi Yusuf.

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Alquran, M., Sulaiman, T.A. & Yusuf, A. Kink-soliton, singular-kink-soliton and singular-periodic solutions for a new two-mode version of the Burger–Huxley model: applications in nerve fibers and liquid crystals. Opt Quant Electron 53, 227 (2021). https://doi.org/10.1007/s11082-021-02883-2

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