  By applying a simple symmetry reduction on a two-layer liquid model, a
nonlocal counterpart of it is obtained. Then a general form of nonlocal
nonlinear Schrodinger (NNLS) equation with shifted parity, charge-conjugate
and delayed time reversal is obtained by using multi-scale expansion method.
Some kinds of elliptic periodic wave solutions of the NNLS equation are
obtained by using function expansion method, which contain soliton solutions
and kink solutions when the modulus taking as unity. Some representative
figures of these solutions are given and analyzed in detail. In addition, by
carrying out the classical symmetry method on the NNLS equation, not only the
Lie symmetry group but also the related symmetry reduction solutions are given.
