All exact solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield equation

We study a 1/4 Bogomol'nyi-Prasad-Sommerfield equation containing configurations made of walls, vortices, and monopoles in the Higgs phase, using the supersymmetric U(N_C) gauge theories with eight supercharges with NF fundamental hypermultiplets. We find the total moduli space to be the quotient of the space of holomorphic maps from the complex plane to the N _C x N_F matrix divided by the space of the holomorphic maps to GL(N_C C). We obtain all possible solutions exactly in the strong coupling limit where the moduli space reduces to the space of all holomorphic maps from a complex plane to the wall moduli space found recently, the deformed complex Grassmann manifold. Monopoles in the Higgs phase are also found in U(1) gauge theory.