A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918495657132032 |
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| author | Li, Zhe |
| author_facet | Li, Zhe |
| contents | Ball lightning is one of the most mysterious atmospheric phenomena, whose long lifetime, penetrative ability, and stability are difficult to explain with traditional physical models. This paper proposes a novel theoretical framework, interpreting ball lightning as a projection of a high-dimensional topological soliton into three-dimensional space. Its essence is described by a nonlinear Schrödinger equation with attractive interaction, protected by a non-zero topological charge. Through numerical simulation of the three-dimensional Gross-Pitaevskii equation, we verify the core predictions of this model: in a Bose-Einstein condensate with attractive interactions, solitons carrying topological charge exhibit: (1)long-lived stability (topological charge conserved under perturbations); (2)low transmission probability (due to minimal overlap integral resulting from orthogonality with the ground state wavefunction); (3)energy and size scales consistent with actual observations. Theoretical analysis indicates that the soliton lifetime is governed by the system's decoherence rate, providing a natural explanation for the observed second-scale lifetimes. This work not only offers a self-consistent physical explanation for ball lightning but also provides a concrete scheme for the experimental preparation and observation of three-dimensional topological solitons. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_09851 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation Li, Zhe Pattern Formation and Solitons Atomic Physics Ball lightning is one of the most mysterious atmospheric phenomena, whose long lifetime, penetrative ability, and stability are difficult to explain with traditional physical models. This paper proposes a novel theoretical framework, interpreting ball lightning as a projection of a high-dimensional topological soliton into three-dimensional space. Its essence is described by a nonlinear Schrödinger equation with attractive interaction, protected by a non-zero topological charge. Through numerical simulation of the three-dimensional Gross-Pitaevskii equation, we verify the core predictions of this model: in a Bose-Einstein condensate with attractive interactions, solitons carrying topological charge exhibit: (1)long-lived stability (topological charge conserved under perturbations); (2)low transmission probability (due to minimal overlap integral resulting from orthogonality with the ground state wavefunction); (3)energy and size scales consistent with actual observations. Theoretical analysis indicates that the soliton lifetime is governed by the system's decoherence rate, providing a natural explanation for the observed second-scale lifetimes. This work not only offers a self-consistent physical explanation for ball lightning but also provides a concrete scheme for the experimental preparation and observation of three-dimensional topological solitons. |
| title | A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation |
| topic | Pattern Formation and Solitons Atomic Physics |
| url | https://arxiv.org/abs/2605.09851 |