The vortex filament equation and a semilinear Schrödinger equation in a Hermitian symmetric space
The vortex filament equation and a semilinear Schrödinger equation in a Hermitian symmetric space
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埃尔米特对称空间中的涡丝方程和半线性薛定谔方程
DOI：
10.18910/9985
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发表时间：
1997
影响因子：
0.4
通讯作者：
N. Koiso
中科院分区：
文献类型：
--
作者：
N. Koiso
本文将证明初值问题古典解的存在唯一性，并将其推广到三维空间形式曲线的情形。我们还考虑了Kahler流形中曲线的相关半线性Schrodinger方程。值得注意的是，我们需要对称空间作为流形，以满足解的无限时间存在性。更准确地说，我们将得到以下结果。
In this paper, we will 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 Schrodinger equations for curves in Kahler manifolds. It is remarkable that we need symmetric spaces as manifolds for infinite time existence of solutions. More precisely, we will get the following results.