Standing Manakov solitons in networks: Exact solutions and stability analysis in metric graphs based approach

We consider the (stationary) time-independent Manakov system on metric graphs. In particular, for the vertex boundary conditions following the conservation laws, we obtain exact soliton solutions of the problem. The ground state solution, i.e., the solution corresponding to a minimum of energy, is studied. The stability of the ground state solution is analyzed using variational approaches.