Solutions of the Yang-Mills-Higgs equations in 2+1 dimensional anti-de Sitter space-time

The solutions of the Bogomolny equation in anti-de Sitter space-time are obtained by using Darboux transformations with both constant spectral parameters and variable “spectral parameters”. These solutions give the Yang-Mills-Higgs fields in anti-de Sitter space-time. Some examples in SU(2) case are considered and qualitative asymptotic behaviors of the solutions as t tends to infinity are discussed in detail.