The vortex filament equation and a semilinear Schrödinger equation in a Hermitian symmetric space
type: Item
instance of: scholarly article
title: The vortex filament equation and a semilinear Schrödinger equation in a Hermitian symmetric space
zbMATH Open document ID: 0926.53002
author: Norihito Koiso
published in: Osaka Journal of Mathematics
publication date: 1997-07-03T00:00:00Z
review text: We consider the initial value problem of the vortex filament equation on \(\mathbb{R}^3\): \[ \gamma_t=\gamma_x\times\gamma_{xx} \] with \(|\gamma_x|\equiv 1\) and \(\times\) denoting the exterior product. We prove the existence and the uniqueness of a classical solution for the initial value problem and generalize it to the case of curves in 3-dimensional space forms. We also consider related semilinear Schrödinger equations for curves in Kähler manifolds. It is remarkable that we need symmetric spaces as manifolds for infinite time existence of solutions.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 58J47
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1014611
zbMATH Keywords: initial value problem
zbMATH Keywords: vortex filament equation
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: curves in 3-dimensional space forms
zbMATH Keywords: semilinear Schrödinger equations
zbMATH Keywords: curves in Kähler manifolds
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1014611