  In this thesis we study dynamic of magnetic monopoles from Lagrangian density
in Yang-Mills-Higgs field theory. In particular, we discuss BPS (Bogomolny
Prasad Sommerfield) magnetic monopoles, described by SU(N) Bogomolny equations,
which has field equations in form of non-linear coupled matrix field equations.
One of the methods to simplify SU(N) Bogomolny equations is by using harmonic
maps $CP^{(N-1)}$. This method has relation with $Gr(n,N)} \sigma$-model and
can transform SU(N) Bogomolny equation into more simple scalar field equations
that depends only on one variable. As an example, we consider the case of SU(2)
Bogomolny equation.
