BIFURCATIONS AND TRAVELING WAVE SOLUTIONS OF THE SPACE-TIME FRACTIONAL COUPLED BOUSSINESQ EQUATIONS

Zhen Zheng, Hui Meng, Jing Zhang and Zenggui Wang
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Zhen Zheng: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Hui Meng: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Jing Zhang: 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), 2025, vol. 33, issue 07, 1-18

Abstract: This paper mainly applies bifurcation theory to study the space-time fractional coupled Boussinesq equations. First, the space-time fractional differential equations with M-truncated derivative are transformed into an ordinary differential equation. Then, the phase portraits of the equation are plotted. Based on the orbits of the phase portraits, different traveling wave solutions are established, including solitary wave solutions, periodic solutions, and singular solutions. Finally, the physical structures of some solutions are plotted with appropriate parameter values. The results show that the novelty of this paper lies in the combination of qualitative theory and quantitative calculation, which makes the paper more comprehensive and systematic. It fills the gaps in the model and yields many new exact traveling wave solutions of the space-time fractional coupled Boussinesq equations that differ from those previously discovered.

Keywords: The Space-Time Fractional Coupled Boussinesq Equations; Bifurcation Analysis; Exact Solutions; M-Truncated Derivative (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500653

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