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

Abstract 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.