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Existence of periodic, solitary and compacton travelling wave solutions of a \((3+1)\)-dimensional time-fractional nonlinear evolution equations with applications

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In this paper, we consider the bifurcation method of dynamical systems for solving time fractional nonlinear evolution equations. We adapt and modify the methodology, incorporating new ideas from the conformable fractional derivative, to investigate exact travelling wave solutions and bifurcations of phase transitions for nonlinear evolution equations. In this study, we show the existence of periodic wave solutions, kink and anti-kink wave solutions, a bright and dark solitary wave solution and parabolic solutions. Moreover, numerical simulations method is applied to show the richer dynamical behavior of the spatial and temporal fractional order of nonlinear evolutions systems and verify the theoretical results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Temesgen Desta Leta, Wenjun Liu &  Jian Ding

  2. Reading Academy, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Temesgen Desta Leta

  3. Department of Mathematics, Dilla University, 419, Dilla, Ethiopia

    Temesgen Desta Leta

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  1. Temesgen Desta Leta
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Temesgen Desta Leta: supported by Talented Young Scientist Program of Ministry of Science and Technology of China (Ethiopia-18-010) and National Natural Science Foundation of China [Grant Number 1191101161]. Wenjun Liu: supported by the National Natural Science Foundation of China [Grant Number 11771216], the Key Research and Development Program of Jiangsu Province (Social Development) [Grant Number BE2019725], and the Six Talent Peaks Project in Jiangsu Province [Grant Number 2015-XCL-020].

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Leta, T.D., Liu, W. & Ding, . Existence of periodic, solitary and compacton travelling wave solutions of a \((3+1)\)-dimensional time-fractional nonlinear evolution equations with applications. Anal.Math.Phys. 11, 34 (2021). https://doi.org/10.1007/s13324-020-00458-0

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