Integrable nonlinear Klein–Gordon systems with [formula omitted] nonlocality and/or space–time exchange nonlocality

Abstract

In additional to the parity (P) symmetric, time reversal (T) symmetric, and PT symmetric nonlocal integrable systems, some other types of nonlocal integrable Klein–Gordon models with the space–time exchange nonlocality and the moving nonlocality are proposed. The Lax pairs of the established nonlinear nonlocal Klein–Gordon equations are explicitly given. A special soliton solution, composed of PT-symmetric part and PT-antisymmetric part, is illustrated with the shape change.