Bifurcation analysis and new waveforms to the fractional KFG equation

Ullah, Mohammad Safi; Ali, M. Zulfikar; Harun-Or-Roshid,

doi:10.1016/j.padiff.2024.100716

Cited by 13 publications

(1 citation statement)

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“…Bifurcation analysis is a robust technique widely used to explore dynamic structures, which has significant implications in various fields [ 27 , 28 ]. The bifurcation process, announced by Liu and Li in 2002 [ 29 ], is a necessary tool for probing the dynamics of nonlinear models.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation, chaos, and stability analysis to the second fractional WBBM model

Ullah,

Ali,

Roshid

2024

PLoS ONE

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This manuscript investigates bifurcation, chaos, and stability analysis for a significant model in the research of shallow water waves, known as the second 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) model. The dynamical system for the above-mentioned nonlinear structure is obtained by employing the Galilean transformation to fulfill the research objectives. Subsequent analysis includes planar dynamic systems techniques to investigate bifurcations, chaos, and sensitivities within the model. Our findings reveal diverse features, including quasi-periodic, periodic, and chaotic motion within the governing nonlinear problem. Additionally, diverse soliton structures, like bright solitons, dark solitons, kink waves, and anti-kink waves, are thoroughly explored through visual illustrations. Interestingly, our results highlight the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. Our techniques’ efficiency, conciseness, and effectiveness advance our understanding of this model and suggest broader applications for exploring nonlinear systems. In addition to improving our understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability, this study reveals insights into dynamic properties and wave patterns.

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Section: Introductionmentioning

confidence: 99%