Non-integrability of Self-dual Yang-Mills-Higgs System
  We examine integrability of self-dual Yang-Mills system in the Higgs phase, with taking simpler cases of vortices and domain walls. We show that the vortex equations and the domain-wall equations do not have Painleve property. This fact suggests that these equations are not integrable. 
Takeo Inami, Shie Minakami (Chuo Univ.) and Muneto Nitta (Keio Univ.)