Doubly periodic soutions in the Chern-Simons gauged O(3) sigma model with a symmetric potential

초록

The Chern-Simons gauged O(3) sigma model was proposed in an attempt to overcome a drawback of the classical O(3) sigma model which describes physical phenomena such as planar ferromagnet. In this talk, we introduce an elliptic governing equation for the CS gauged O(3) sigma model with doubly periodic boundary condition on a periodic lattice cell in R^2. The governing equation has positive and negative singular sources unlike the well-known Chern-Simons-Higgs vortex equation, and it is known to admit two different kinds of solutions. We would like to show the existence and asymptotic behavior of solutions as the coupling parameter tends to zero. Uniqueness will be also discussed.