  We analytically construct vortex solutions in the integrable sector of the
extended Skyrme-Faddeev model. The solutions are holomorphic type which satisfy
the zero curvature condition. For the model parameter $\beta e^2=1$ there is a
lump solution, and for $\beta e^2 \neq 1$ new potentials are introduced for the
several molecular-shaped solutions with half-integer or integer charges. They
necessarily have infinite number of conserved currents and some of the examples
are shown. By performing an annealing simulation with our potentials, we verify
the existence of the solutions of the integrable sector.
