| This thesis is divided into two parts.The first part is devoted to the study of an Abelian-Higgs model arising from the Aharony-Bergman-Jafferis-Maldacena(ABJM)theory,for which the Euler-Lagrange equations of the energy functional are a system of second-order nonlinear ordinary differential equations.We firstly prove the equivalence of Euler-Lagrange equations and the first-order equations(BPS equations)by analytical method.Then we prove the equivalence of BPS system and a single equation.Finally we present the explicit solutions of the problem.Our results show that the Abelianization Ansatz used for the ABJM model in[2]is not suitable.The second part is concentrated on the study of the self-dual monopole problem arising in gauge field theory.Within the radially symmetric case,we establish the existence and uniqueness theorem for this problem by using use a dynamic shooting method.At last,the asymptotic estimates of solutions are obtained by analytic methods. |
