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Soliton Solutions of \((2+1)\) Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational \(sine-cosine\) and \(sinh-cosh\) Method

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Abstract

In this research, our main motivation is to find the novel analytical solutions of \((2+1)\) dimensional Heisenberg ferromagnetic spin equation, which describes the nonlinear dynamics of the ferromagnetic materials by using the extended rational \(sine-cosine\) and \(sinh-cosh\) methods. The considered PDE is converted to an ODE by applying a wave transformation, and then the solutions of the ODE are supposed to be in the rational forms of trigonometric functions. After substituting the solutions to the ODE and doing some basic calculations, a system of algebraic equations is derived. So, finding the solutions of the PDE turns into a problem of solving an algebraic system of equations. The unknown coefficients in the solutions that are in the rational form are found by solving the obtained system. The methods are powerful and can be applied to find exact solutions to lots of PDEs in mathematical physics.

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Acknowledgements

Melih Cinar would like to thank the Scientific and Technological Research Council of Turkey (TUBITAK) for the financial support of the 2211-A Fellowship Program.

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Authors and Affiliations

  1. Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey

    Melih Cinar, Ismail Onder & Aydin Secer

  2. Graduate School of Natural and Aplied Sciences, Yildiz Technical University, Istanbul, Turkey

    Melih Cinar

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

    Abdullahi Yusuf, Tukur Abdulkadir Sulaiman & Mustafa Bayram

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

    Abdullahi Yusuf & Tukur Abdulkadir Sulaiman

  5. Department of Mathematics and Science Education, Biruni University, Istanbul, Turkey

    Huseyin Aydin

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  1. Melih Cinar
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  2. Ismail Onder
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  3. Aydin Secer
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  4. Abdullahi Yusuf
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  5. Tukur Abdulkadir Sulaiman
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  7. Huseyin Aydin
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Correspondence to Mustafa Bayram.

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Cinar, M., Onder, I., Secer, A. et al. Soliton Solutions of \((2+1)\) Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational \(sine-cosine\) and \(sinh-cosh\) Method. Int. J. Appl. Comput. Math 7, 135 (2021). https://doi.org/10.1007/s40819-021-01076-5

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