Explicit Blowing-up Solutions to the Schr\"odinger Maps from ${\bf R}^2$ to the Hyperbolic 2-Space ${\bf H}^2$
Ding, Qing
arXiv, 0312028 / Harvested from arXiv
Text on arXiv
In this article, we prove that the equation of the Schr\"odinger maps from ${\bf R}^2$ to the hyperbolic 2-space ${\bf H}^2$ is SU(1,1)-gauge equivalent to the following 1+2 dimensional nonlinear Schr\"odinger-type system of unknown three complex functions $p,q,r$ and a real function $u$: {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\qquad
Publié le : 2003-12-01
Classification:  Mathematics - Differential Geometry,  Mathematical Physics,  53C44 (Primary), 35Q55 (Secondary) 
@article{0312028,
     author = {Ding, Qing},
     title = {Explicit Blowing-up Solutions to the Schr\"odinger Maps from ${\bf R}^2$
  to the Hyperbolic 2-Space ${\bf H}^2$},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312028}
}

Ding, Qing. Explicit Blowing-up Solutions to the Schr\"odinger Maps from ${\bf R}^2$
  to the Hyperbolic 2-Space ${\bf H}^2$. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312028/