Exact, molecular-shaped vortices with fractional and integer charges in the extended Skyrme-Faddeev model

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.