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Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations

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  • Zhao Li
  • Peng Li
  • Tianyong Han
  • Abdul Qadeer Khan

Abstract

In this paper, the bifurcation, phase portraits, traveling wave solutions, and stability analysis of the fractional generalized Hirota–Satsuma coupled KdV equations are investigated by utilizing the bifurcation theory. Firstly, the fractional generalized Hirota–Satsuma coupled KdV equations are transformed into two-dimensional Hamiltonian system by traveling wave transformation and the bifurcation theory. Then, the traveling wave solutions of the fractional generalized Hirota–Satsuma coupled KdV equations corresponding to phase orbits are easily obtained by applying the method of planar dynamical systems; these solutions include not only the bell solitary wave solutions, kink solitary wave solutions, anti-kink solitary wave solutions, and periodic wave solutions but also Jacobian elliptic function solutions. Finally, the stability criteria of the generalized Hirota–Satsuma coupled KdV equations are given.

Suggested Citation

  • Zhao Li & Peng Li & Tianyong Han & Abdul Qadeer Khan, 2021. "Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-6, October.
    • Handle: RePEc:hin:jnddns:5303295
    DOI: 10.1155/2021/5303295
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    Cited by:

    1. Li, Zhao & Huang, Chun, 2023. "Bifurcation, phase portrait, chaotic pattern and optical soliton solutions of the conformable Fokas–Lenells model in optical fibers," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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