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We have considered cubic nonlinear Schr\"odinger equation along withsupersymmetric $\mathcal{PT}$ like potential and obtained exact stationarysolutions in terms of bright and brigh-dark interacting solitons. The$\mathcal{PT}$ broken and $\mathcal{PT}$ unbroken regions are demonstrated alsodepicted. Connected and disconnected stable regions of bright and dark solitonsare examined incorporating linear stability analysis validated by directnumerical simulations. Moreover, the strength of stability has been illustratedthrough excitations of bright and dark solitons.

Connected and disconnected stable regions of solitons of nonlinear Schr\"odinger equation with $\mathcal{PT}$-symmetric potential