A Numerical Study of the Self-Similar Solutions of the Schrödinger Map
Copyright policy )A Numerical Study of the Self-Similar Solutions of the Schrödinger Map
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.
- University of California, Santa Barbara United States
- University of the Basque Country Spain
NLS equations (nonlinear Schrödinger equations), Numerical Analysis (math.NA), Vortex flows for incompressible inviscid fluids, self-similar solution, Vortex methods applied to problems in fluid mechanics, 35Q55, 65D10, 65N35, 65T50, 76B47, collocation method, Mathematics - Analysis of PDEs, FOS: Mathematics, localized induction approximation, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Schrödinger map, Numerical methods for discrete and fast Fourier transforms, formation of singularities, Analysis of PDEs (math.AP)
NLS equations (nonlinear Schrödinger equations), Numerical Analysis (math.NA), Vortex flows for incompressible inviscid fluids, self-similar solution, Vortex methods applied to problems in fluid mechanics, 35Q55, 65D10, 65N35, 65T50, 76B47, collocation method, Mathematics - Analysis of PDEs, FOS: Mathematics, localized induction approximation, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Schrödinger map, Numerical methods for discrete and fast Fourier transforms, formation of singularities, Analysis of PDEs (math.AP)
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