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General soliton solutions to a nonlocal nonlinear Schr\"odinger (NLS)equation with PT-symmetry for both zero and nonzero boundary conditions {areconsidered} via the combination of Hirota's bilinear method and theKadomtsev-Petviashvili (KP) hierarchy reduction method. First, general$N$-soliton solutions with zero boundary conditions are constructed. Startingfrom the tau functions of the two-component KP hierarchy, it is shown that theycan be expressed in terms of either Gramian or double Wronskian determinants.On the contrary, from the tau functions of single component KP hierarchy,general soliton solutions to the nonlocal NLS equation with nonzero boundaryconditions are obtained. All possible soliton solutions to nonlocal NLS withParity (PT)-symmetry for both zero and nonzero boundary conditions are found inthe present paper.

General soliton solution to a nonlocal nonlinear Schr\"odinger equation with zero and nonzero boundary conditions