Zhang, K., Zhang, Z. and Yuwen, T. (2022) Phase Portraits and Traveling Wave Solutions of a Fractional Generalized Reaction Duffing Equation. Advances in Pure Mathematics, 12, 465-477.
https://doi.org/10.4236/apm.2022.127035

has been cited by the following article:

• TITLE: Exact Traveling Wave Solutions of the Generalized Fractional Differential mBBM Equation

  AUTHORS: Yuting Zhong, Renzhi Lu, Heng Su

  KEYWORDS: A Generalized Fractional Differential mBBM Equation, Traveling Wave Solution, Phase Portrait

  JOURNAL NAME: Advances in Pure Mathematics, Vol.13 No.3, March 17, 2023

  ABSTRACT: By using the fractional complex transform and the bifurcation theory to the generalized fractional differential mBBM equation, we first transform this fractional equation into a plane dynamic system, and then find its equilibrium points and first integral. Based on this, the phase portraits of the corresponding plane dynamic system are given. According to the phase diagram characteristics of the dynamic system, the periodic solution corresponds to the limit cycle or periodic closed orbit. Therefore, according to the phase portraits and the properties of elliptic functions, we obtain exact explicit parametric expressions of smooth periodic wave solutions. This method can also be applied to other fractional equations.