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The generalized bifurcation method for deriving exact solutions of nonlinear space-time fractional partial differential equations

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  • Wen, Zhenshu

Abstract

In this paper, we develop a generalized bifurcation method to study exact solutions of nonlinear space-time fractional partial differential equations (PDEs), which is based on the bifurcation theory of dynamical systems. We present the procedure of the method and illustrate it with application to the space-time fractional Drinfel’d–Sokolov–Wilson equation. We identify all bifurcation conditions and derive the phase portraits of the system, from which we obtain different new exact solutions, and more interestingly, we find the so-called M/W-shaped solitary wave solutions. The results demonstrate the efficiency of the method in deriving exact solutions of space-time fractional PDEs.

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  • Wen, Zhenshu, 2020. "The generalized bifurcation method for deriving exact solutions of nonlinear space-time fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307271
    DOI: 10.1016/j.amc.2019.124735
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    1. Yao, Yuqin, 2005. "Abundant families of new traveling wave solutions for the coupled Drinfel’d–Sokolov–Wilson equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 301-307.
    2. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
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    Cited by:

    1. Bakıcıerler, Gizel & Alfaqeih, Suliman & Mısırlı, Emine, 2021. "Analytic solutions of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    2. Constantin Bota & Bogdan Căruntu & Dumitru Ţucu & Marioara Lăpădat & Mădălina Sofia Paşca, 2020. "A Least Squares Differential Quadrature Method for a Class of Nonlinear Partial Differential Equations of Fractional Order," Mathematics, MDPI, vol. 8(8), pages 1-12, August.

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