Some special exact solutions in nonlocal Alice-Bob sine-Gordon systems


 Three nonlocal Alice–Bob sine-Gordon (ABSG) systems with the parity and time reversal nonlocality and/or space-time exchange nonlocality are investigated. For the common local SG equation, two types of N-soliton solutions and three types of periodic solutions are presented. The multiple solutions, breather solution, double knot solution and periodic solutions of the ABSG systems are obtained from the symmetry reductions of a coupled local sine-Gordon system.