Unveiling solitons and dynamic patterns for a (3+1)-dimensional model describing nonlinear wave motion

Muhammad Bilal Riaz; Syeda Sarwat Kazmi; Adil Jhangeer; Jan Martinovic; Muhammad Bilal Riaz; Syeda Sarwat Kazmi; Adil Jhangeer; Jan Martinovic

doi:10.3934/math.2024992

AIMS Mathematics

2024, Volume 9, Issue 8: 20390-20412. doi: 10.3934/math.2024992

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Unveiling solitons and dynamic patterns for a (3+1)-dimensional model describing nonlinear wave motion

1.
IT4 Innovations, VSB–Technical University of Ostrava, Ostrava, Czech Republic
2.
Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
3.
Department of Mathematics, Namal University, Talagang Road, Mianwali 42250, Pakistan

Received: 17 March 2024 Revised: 29 April 2024 Accepted: 07 May 2024 Published: 24 June 2024
MSC : 34H10, 35C08

In this study, the underlying traits of the new wave equation in extended (3+1) dimensions, utilized in the field of plasma physics and fluids to comprehend nonlinear wave scenarios in various physical systems, were explored. Furthermore, this investigation enhanced comprehension of the characteristics of nonlinear waves present in seas and oceans. The analytical solutions of models under consideration were retrieved using the sub-equation approach and Sardar sub-equation approach. A diverse range of solitons, including bright, dark, combined dark-bright, and periodic singular solitons, was made available through the proposed methods. These solutions were illustrated through visual depictions utilizing 2D, 3D, and density plots with carefully chosen parameters. Subsequently, an analysis of the dynamical nature of the model was undertaken, encompassing various aspects such as bifurcation, chaos, and sensitivity. Bifurcation analysis was conducted via phase portraits at critical points, revealing the system's transition dynamics. Introducing an external periodic force induced chaotic phenomena in the dynamical system, which were visualized through time plots, two-dimensional plots, three-dimensional plots, and the presentation of Lyapunov exponents. Furthermore, the sensitivity analysis of the investigated model was executed utilizing the Runge-Kutta method. The obtained findings indicated the efficacy of the presented approaches for analyzing phase portraits and solitons over a wider range of nonlinear systems.
- new integrable wave equation,
- soliton solutions,
- sub-equation method,
- Sardar sub-equation method,
- bifurcation,
- chaotic behavior,
- sensitivity
Citation: Muhammad Bilal Riaz, Syeda Sarwat Kazmi, Adil Jhangeer, Jan Martinovic. Unveiling solitons and dynamic patterns for a (3+1)-dimensional model describing nonlinear wave motion[J]. AIMS Mathematics, 2024, 9(8): 20390-20412. doi: 10.3934/math.2024992

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Abstract

In this study, the underlying traits of the new wave equation in extended (3+1) dimensions, utilized in the field of plasma physics and fluids to comprehend nonlinear wave scenarios in various physical systems, were explored. Furthermore, this investigation enhanced comprehension of the characteristics of nonlinear waves present in seas and oceans. The analytical solutions of models under consideration were retrieved using the sub-equation approach and Sardar sub-equation approach. A diverse range of solitons, including bright, dark, combined dark-bright, and periodic singular solitons, was made available through the proposed methods. These solutions were illustrated through visual depictions utilizing 2D, 3D, and density plots with carefully chosen parameters. Subsequently, an analysis of the dynamical nature of the model was undertaken, encompassing various aspects such as bifurcation, chaos, and sensitivity. Bifurcation analysis was conducted via phase portraits at critical points, revealing the system's transition dynamics. Introducing an external periodic force induced chaotic phenomena in the dynamical system, which were visualized through time plots, two-dimensional plots, three-dimensional plots, and the presentation of Lyapunov exponents. Furthermore, the sensitivity analysis of the investigated model was executed utilizing the Runge-Kutta method. The obtained findings indicated the efficacy of the presented approaches for analyzing phase portraits and solitons over a wider range of nonlinear systems.

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