Unveiling Hirota–Maccari model dynamics via diverse elegant methods

Akter, Mahinur; Ullah, Mohammad Safi; Wazwaz, Abdul-Majid; Seadawy, Aly R.

doi:10.1007/s11082-024-06714-y

Cited by 14 publications

(1 citation statement)

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“…Consequently, the attraction of soliton solutions in the field of mathematical physics is considerable [ 7 , 8 ]. Many distinguished nonlinear models provide evidence of the presence of these soliton outcomes like the Jimbo-Miwa structure [ 9 ], Phi-4 equation [ 10 ], the extended Boussinesq nonlinear framework [ 11 ], the Nizhnik-Novikov-Veselov model [ 12 ], the ISLW system [ 13 ], the 3D fractional WBBM structure [ 14 ], Fokas-Lenells system [ 15 ], and various others [ 16 – 18 ]. Nonlinear models can be solved using a variety of effective methods, and soliton outcomes can be obtained.…”

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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