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For a number of nonlocal nonlinear equations such as nonlocal, nonlinearSchr\"odinger equation (NLSE), nonlocal Ablowitz-Ladik (AL), nonlocal,saturable discrete NLSE (DNLSE), coupled nonlocal NLSE, coupled nonlocal AL andcoupled nonlocal, saturable DNLSE, we obtain periodic solutions in terms ofJacobi elliptic functions as well as the corresponding hyperbolic solitonsolutions. Remarkably, in all the six cases, we find that unlike thecorresponding local cases, all the nonlocal models simultaneously admit boththe bright and the dark soliton solutions. Further, in all the six cases, notonly $\dn(x,m)$ and $\cn(x,m)$ but even their linear superposition is shown tobe an exact solution. Finally, we show that the coupled nonlocal NLSE not onlyadmits solutions in terms of Lam\'e polynomials of order 1, but it also admitssolutions in terms of Lam\'e polynomials of order 2, even though they are notthe solutions of the uncoupled nonlocal problem. We also remark on the possibleintegrability in certain cases.

Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations