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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2508.01816 |
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| _version_ | 1866916890978287616 |
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| author | Dutta, Saugata Mondal, Kajal Kumar Chatterjee, Prasanta |
| author_facet | Dutta, Saugata Mondal, Kajal Kumar Chatterjee, Prasanta |
| contents | This work presents a detailed analytical and geometrical investigation of the (2+1)-dimensional Boiti-Leon-Pempinelli system, a nonlinear dispersive model arising in the context of fluid and plasma dynamics. By employing a projective Riccati-based ansatz, a new class of exact solutions is systematically derived. These solutions, when visualized, exhibit intricate geometrical features that evolve across multiple spatial scales. To quantify this complexity, a voxel-based box-counting dimension analysis is conducted on the corresponding surface profiles. The analysis reveals non-integer fractal dimensions that vary with magnification, confirming the self-affine nature of the patterns and highlighting the multiscale structure inherent in the system. Such fractal character is not only of theoretical interest but also reflects real-world behaviors in turbulent plasma flows and fine-scale fluid instabilities. The study thus bridges exact analytical solutions with computational fractal geometry, providing a deeper understanding of the BLP system and its relevance in describing natural phenomena characterized by spatial complexity and multiscale interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractal Dimension in Nonlinear Wave Dynamics Governed by a Nonlinear Partial Differential Equation Dutta, Saugata Mondal, Kajal Kumar Chatterjee, Prasanta Mathematical Physics This work presents a detailed analytical and geometrical investigation of the (2+1)-dimensional Boiti-Leon-Pempinelli system, a nonlinear dispersive model arising in the context of fluid and plasma dynamics. By employing a projective Riccati-based ansatz, a new class of exact solutions is systematically derived. These solutions, when visualized, exhibit intricate geometrical features that evolve across multiple spatial scales. To quantify this complexity, a voxel-based box-counting dimension analysis is conducted on the corresponding surface profiles. The analysis reveals non-integer fractal dimensions that vary with magnification, confirming the self-affine nature of the patterns and highlighting the multiscale structure inherent in the system. Such fractal character is not only of theoretical interest but also reflects real-world behaviors in turbulent plasma flows and fine-scale fluid instabilities. The study thus bridges exact analytical solutions with computational fractal geometry, providing a deeper understanding of the BLP system and its relevance in describing natural phenomena characterized by spatial complexity and multiscale interactions. |
| title | Fractal Dimension in Nonlinear Wave Dynamics Governed by a Nonlinear Partial Differential Equation |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2508.01816 |