In this talk some recent progress in non-Abelian Chern--Simons--Higgs vortex equations will be presented. Firstly, we will review some elliptic pdes with related results originated from classical Abelian Higgs and Chern--Simons--Higgs models. Secondly, we will report an existence theorem concerning the existence of doubly periodic solutions for the non-abelian Chern--Simons--Higgs vortex equations with a sketch of proof. At last, we mention some related problems and open questions.
Biography
Professor Xiaosen Han holds his Ph.D. from Southeast University in 2009. Now he is an associate professor in School of Mathematical and Statistics, Henan University. His research interests are nonlinear partial differential equations and nonlinear analysis, especially the nonlinear pdes arising in theoretical physics.