从${\bf R}^2$到双曲2-空间${\bf H}^2$的Schr"odinger映射的显式爆裂解
微分几何
2009-06-01 v3 数学物理
math.MP
摘要
在本文中，我们证明从到双曲2-空间的Schr"odinger映射方程SU(1,1)-规范等价于如下未知三个复函数与一个实函数的1+2维非线性Schr"odinger型方程组：{c} iq_t+q_{z{\bar z}}-2u q+2({\bar p}q)_z-2pq_{\bar z}-4|p|^2q=0\qquad ir_t-r_{z{\bar z}}+2u r+2({\bar p}r)_z-2pr_{\bar z}+4|p|^2r=0\qquad ip_t+(qr)_{\bar z}-u_z=0\qquad\qquad\qquad\qquad\qquad
引用
@article{arxiv.math/0312028,
title = {Explicit Blowing-up Solutions to the Schr\"odinger Maps from ${\bf R}^2$ to the Hyperbolic 2-Space ${\bf H}^2$},
author = {Qing Ding},
journal= {arXiv preprint arXiv:math/0312028},
year = {2009}
}
备注
21 pages without figures