Self-similar solutions for the 1D Schrödinger map on the hyperbolic plane

DOI10.1007/s00209-007-0115-6zbMath1128.35099OpenAlexW2064477376MaRDI QIDQ2384739

Francisco de la Hoz

Publication date: 10 October 2007

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-007-0115-6

zbMATH Keywords

singularitiesnonlinear Schrödinger equationMinkowski 3-spacevortex filamentlocalized induction approximation

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (10)

On the relationship between the one-corner problem and the \(M\)-corner problem for the vortex filament equation ⋮ On the stability of a singular vortex dynamics ⋮ Stability of the self-similar dynamics of a vortex filament ⋮ Scattering for 1D cubic NLS and singular vortex dynamics ⋮ On the Dirac delta as initial condition for nonlinear Schrödinger equations ⋮ Vortex filament equation for a regular polygon in the hyperbolic plane ⋮ Parabolic curves in Lie groups ⋮ On the Schrödinger map for regular helical polygons in the hyperbolic space ⋮ The dynamics of vortex filaments with corners ⋮ The vortex filament equation as a pseudorandom generator

Cites Work

• Unnamed Item
• A note on the NLS and the Schrödinger flow of maps
• Formation of Singularities and Self-Similar Vortex Motion Under the Localized Induction Approximation†
• The gauge equivalence of the NLS and the Schrödinger flow of maps in 2 + 1 dimensions
• On the curvature and torsion of an isolated vortex filament
• A soliton on a vortex filament

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