Existence of dnoidal-type standing waves on the loop coupled to soliton tails on half-lines is shown via the Implicit Function Theorem, with orbital (in)stability analyzed using perturbation and Krein-von Neumann theory.
Cacciapuoti,Existence of the ground state for the NLS with potential on graphs, Contem- porary Mathematics, Mathematical Problems in Quantum Physics, 717, (2018), 155-172
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Existence and (in)stability of standing waves for the nonlinear Schr\"odinger Equations on looping-edge graphs with $\delta'$-type interactions
Existence of dnoidal-type standing waves on the loop coupled to soliton tails on half-lines is shown via the Implicit Function Theorem, with orbital (in)stability analyzed using perturbation and Krein-von Neumann theory.