Pitaevskii
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Related Articles from SNS
Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains
Announce Type: replace Abstract: This paper introduces the Stochastic-Dimension Frozen Sampled Neural Network (SD-FSNN), a novel computational framework for solving high-dimensional Gross-Pitaevskii equation (GPE) on unbounded domain. The proposed method circumvents the curse-of-dimensionality that plagues traditional discretizations and the computational bottlenecks of gradient-based neural network solvers through a synergistic combination of techniques. First, a prescribed Gaussian...
On the Gurevich-Pitaevskii solution of KdV
Announce Type: cross Abstract: The universal solution of the Korteweg-de Vries equation (KdV) introduced by Gurevich and Pitaevskii in order to describe the onset of dispersive shock waves is known to also obey the self-similar reduction of the next member in the KdV hierarchy. We show that, if this common solution obeys some lower order partial differential equation, its differential order must be one, and we provide its local representation as a converging Laurent series depending on both...
A Topological Soliton Model for Ball Lightning: Theory and Numerical Verification with the 3D Gross-Pitaevskii Equation
Announce Type: replace-cross 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 Schr\"odinger equation with attractive interactions, stabilized by a non-zero topological charge.