Robin spectral determinant for defocusing NLS ($\mathcal{D}(k)=(2k+ic)a(k)a^{♯}(-k)+(2k-ic)b(k)b^{♯}(-k)$)

The effective boundary coefficient is $\tilde{\Gamma }=-(2k-ic)b^{♯}(-k)/(a\mathcal{D})$. All its ingredients come from initial scattering and the Robin boundary condition. Genuine zeros produce pole data; common zeros in numerator and denominator can instead be removable. It is incorrect to assert absence of boundary poles for every real Robin parameter.