Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits
In this study, we investigate the deeper characteristics of the modified Ito equation, which can be applied across various scientific domains to represent systems influenced by noise and randomness. Multi-solitons, including 1-wave, 2-wave, and 3-wave solitons, have been successfully generated using...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003127 |
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| author | Muhammad Bilal Riaz Adil Jhangeer Tomas Kozubek Syeda Sarwat Kazmi |
| author_facet | Muhammad Bilal Riaz Adil Jhangeer Tomas Kozubek Syeda Sarwat Kazmi |
| author_sort | Muhammad Bilal Riaz |
| collection | DOAJ |
| description | In this study, we investigate the deeper characteristics of the modified Ito equation, which can be applied across various scientific domains to represent systems influenced by noise and randomness. Multi-solitons, including 1-wave, 2-wave, and 3-wave solitons, have been successfully generated using a multiple exponential-function approach. For visual representation, the outcomes are displayed through 3D, 2D, density, and contour plots. The wave transformation is then applied to convert the studied model into an ordinary differential equation. Following this, the dynamic nature of the model is examined from various viewpoints, including bifurcation, chaotic phenomena, multistability, and sensitivity analysis. Bifurcation shows how the solution of a planar system depends on equilibrium points, and when an outward periodic force is implemented to the unperturbed planar system, it reveals chaotic characteristics. These are analyzed using tools such as 3-dimensional and 2-dimensional plots, time scale plots, and Poincaré maps. Additionally, the model’s sensitivity is assessed with varying initial values. The results underscore the effectiveness and relevance of the proposed approaches for examining solitons within a broad spectrum of nonlinear systems. |
| format | Article |
| id | doaj-art-6e40a9f7907b444ead00a893358efb0c |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-6e40a9f7907b444ead00a893358efb0c2024-12-13T11:05:35ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112100926Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraitsMuhammad Bilal Riaz0Adil Jhangeer1Tomas Kozubek2Syeda Sarwat Kazmi3IT4Innovations, VSB - Technical University of Ostrava, Ostrava, Czech Republic; Department of Computer Science and Mathematics, Lebanese American University, Byblos, LebanonIT4Innovations, VSB - Technical University of Ostrava, Ostrava, Czech RepublicIT4Innovations, VSB - Technical University of Ostrava, Ostrava, Czech RepublicIT4Innovations, VSB - Technical University of Ostrava, Ostrava, Czech Republic; Corresponding author.In this study, we investigate the deeper characteristics of the modified Ito equation, which can be applied across various scientific domains to represent systems influenced by noise and randomness. Multi-solitons, including 1-wave, 2-wave, and 3-wave solitons, have been successfully generated using a multiple exponential-function approach. For visual representation, the outcomes are displayed through 3D, 2D, density, and contour plots. The wave transformation is then applied to convert the studied model into an ordinary differential equation. Following this, the dynamic nature of the model is examined from various viewpoints, including bifurcation, chaotic phenomena, multistability, and sensitivity analysis. Bifurcation shows how the solution of a planar system depends on equilibrium points, and when an outward periodic force is implemented to the unperturbed planar system, it reveals chaotic characteristics. These are analyzed using tools such as 3-dimensional and 2-dimensional plots, time scale plots, and Poincaré maps. Additionally, the model’s sensitivity is assessed with varying initial values. The results underscore the effectiveness and relevance of the proposed approaches for examining solitons within a broad spectrum of nonlinear systems.http://www.sciencedirect.com/science/article/pii/S2666818124003127The (3+1)-dimensional Ito equationMultiple exponential-function approachBifurcation analysisChaos theorySensitivity analysis |
| spellingShingle | Muhammad Bilal Riaz Adil Jhangeer Tomas Kozubek Syeda Sarwat Kazmi Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits Partial Differential Equations in Applied Mathematics The (3+1)-dimensional Ito equation Multiple exponential-function approach Bifurcation analysis Chaos theory Sensitivity analysis |
| title | Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits |
| title_full | Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits |
| title_fullStr | Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits |
| title_full_unstemmed | Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits |
| title_short | Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits |
| title_sort | investigating multi soliton patterns and dynamical characteristics of the 3 1 dimensional equation via phase portraits |
| topic | The (3+1)-dimensional Ito equation Multiple exponential-function approach Bifurcation analysis Chaos theory Sensitivity analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003127 |
| work_keys_str_mv | AT muhammadbilalriaz investigatingmultisolitonpatternsanddynamicalcharacteristicsofthe31dimensionalequationviaphaseportraits AT adiljhangeer investigatingmultisolitonpatternsanddynamicalcharacteristicsofthe31dimensionalequationviaphaseportraits AT tomaskozubek investigatingmultisolitonpatternsanddynamicalcharacteristicsofthe31dimensionalequationviaphaseportraits AT syedasarwatkazmi investigatingmultisolitonpatternsanddynamicalcharacteristicsofthe31dimensionalequationviaphaseportraits |