Abstract
Some nonlocal sine-Gordon (SG) systems with some different types of nonlocalities are derived from the usual local SG equation by means of the consistent correlated bang approach. The nonlocal SG systems are Lax integrable. Two types of N-soliton solutions and six types of periodic solutions of the usual SG equation are presented. Some types of solutions of the nonlocal integrable SG systems are obtained by using the symmetric-antisymmetric separation approach. Usually, the linear superposition principle can not hold as a general principle in the presence of nonlinearity. In this paper, it is shown that for a special type of nonlocal SG equations, a linear superposition theorem can be survived for some special types of exact solutions.
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