A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation

Abstract

Ball lightning remains one of the most enigmatic atmospheric phenomena, characterized by its long lifetime, ability to penetrate materials, and stable spherical structure. Here we propose a novel theoretical framework interpreting ball lightning as a three-dimensional projection of a high-dimensional topological soliton. The system is described by a nonlinear Schrödinger equation with attractive interactions, stabilized by a non-zero topological charge. Through comprehensive numerical simulations of the three-dimensional Gross-Pitaevskii equation, we verify the model's core predictions: (1) long-lived stability protected by topological invariants, (2) low transmission probability due to wavefunction orthogonality, and (3) energy and size scales consistent with observational data. The soliton lifetime $τ\sim \hbar/Γ$ naturally explains the observed second-scale durations. Our work provides a self-consistent physical explanation for ball lightning while offering concrete pathways for experimental realization of three-dimensional topological solitons in Bose-Einstein condensates and nonlinear optical systems. This theoretical framework gains additional support from recent experimental breakthroughs in laboratory generation of ball-lightning-like structures.