BIFURCATION AND EXACT TRAVELING WAVE SOLUTIONS OF FRACTIONAL DATE–JIMBO–KASHIWARA–MIWA EQUATION

Hui Xu, Minyuan Liu and Zenggui Wang
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Hui Xu: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Minyuan Liu: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Zenggui Wang: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 06, 1-17

Abstract: Based on the bifurcation theory, the exact solutions of fractional Date–Jimbo–Kashiwara–Miwa equation are constructed. In terms of β-derivative, a nonlinear integer-order ODE is obtained, the equation is transformed into a plane dynamical system. The phase portraits are obtained under different bifurcation conditions. According to the orbits of the phase portraits, new bright and dark solitary solutions, periodic solutions, periodic-singular solutions, and singular solutions are established, enriching the diversity of solutions. In addition, the dynamical behaviors of various types of solutions are shown by selecting appropriate parameters, which is useful for understanding the fluctuation behavior in physical models. Compared with previous literature, this paper focuses on the combination of qualitative analyses and qualitative calculations, which makes the paper more systematic and comprehensive, and fills the gap of using bifurcation theory to solve the FDJKM equation. The dynamical behavior of new solutions obtained will provide more and more attractive and complex physical phenomena to explore more mysteries.

Keywords: Plane Dynamical System Theory; β-Derivative; Solitary Solution; Periodic Solution; Singular Solution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24501160

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