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Exact Traveling Wave Solutions of the Generalized Fractional Differential mBBM Equation
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
- 1 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
- 2 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
- 3 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
Advances in Pure Mathematics·Volume 13 (2023)·Pages 167–173·Published 15 March 2023·DOI10.4236/apm.2023.133009
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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.
KeywordsA Generalized Fractional Differential mBBM EquationTraveling Wave SolutionPhase Portrait
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