Two-solitons with logarithmic separation for 1D NLS with repulsive delta potential

We consider the one-dimensional nonlinear Schrödinger equation with focusing, power nonlinearity, and a repulsive delta potential. We show that if the potential is not too strong, the construction by Nguy\~{ê}n (2019) of solutions converging strongly at time infinity to a pair of logarithmically separating solitons can be adapted to accommodate the effect of the potential. On the other hand, we show that if the potential is stronger, no such solutions exist.