A numerical study of the self-similar solutions of the Schroedinger Map

2008/12/04 by de la Hoz, Francisco, Carlos J. Garcı́a-Cervera, Luis Vega +2 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #35Q55 #65D10 #65N35 #65T50 #76B47 #Analysis of PDEs (math.AP) #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Nonlinear Dynamics and Pattern Formation #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0812.1011

openalex publication_date 2008/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a numerical study of the self-similar solutions of the Localized Induction Approximation of a vortex filament. These self-similar solutions, which constitute a one-parameter family, develop a singularity at finite time. We study a number of boundary conditions that allow us reproduce the mechanism of singularity formation. Some related questions are also considered.

Cited by

• Scattering for 1D cubic NLS and singular vortex dynamics

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