  We try to calculate the interaction between vortices in the color-flavor
locked (CFL) phase of Quantum Chromodynamics (QCD). The most fundamental
strings in high density color superconductivity are the non-abelian semi-super
fluid strings. Using Abrikosov ansatz, one can show that the interaction
between these vortices has a universal repulsion form when they are far from
each other. The Ginzburg-Landau (GL) Lagrangian of CFL phase may be compared
with the Lagrangian of Quantum Electrodynamics (QED) with three condensation
states. The behavior of vortices of multi-component superconductivity, within
the framework of GL theory was done for two condensation states ($\rm{MgB_2}$
superconductors) by variational method. The interaction between these vortices
is attractive when they are far from each other and repulsive when they get
close. We attempt to obtain the interaction between these vortices in such
substances using numerical variational method for three condensation states
(Fe-based superconductors). The ultimate aim of the research is to apply these
calculations to the vortices in the color-flavor locked phase of QCD to be able
to study the interaction between them.
