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Zhong, Y., Lu, R. and Su, H. (2023) Exact Traveling Wave Solutions of the Generalized Fractional Differential mBBM Equation. Advances in Pure Mathematics, 13, 167-173.
https://doi.org/10.4236/apm.2023.133009

has been cited by the following article:

• TITLE: Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

  AUTHORS: Dahe Feng, Jibin Li, Airen Zhou

  KEYWORDS: (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation, Bifurcations, Phase Portrait, Analytical Periodic Wave Solution, Periodic Cusp Wave Solution

  JOURNAL NAME: Applied Mathematics, Vol.15 No.8, August 19, 2024

  ABSTRACT: For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.