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The -dimensional integrable reverse space–time nonlocal Schrödinger equation is investigated. It has many applications in fluid mechanics, quantum mechanics and plasma physics. The one-periodic wave solution and two kinds of two-periodic wave solutions are obtained via the bilinear method. Taking a long-wave limit of the periodic wave solutions generates two types of rogue waves, which are called kink-shaped and W-shaped line rogue waves. We also employ the asymptotic analysis to interpret the dynamical properties of the kink-shaped rogue wave. The higher-order rogue waves are generated by the interaction of the above two types of rogue waves. Their plots exhibit interesting patterns with several different outlines. Furthermore, the semirational solutions are obtained, which arise from the interactions between rogue waves and the periodic line wave. They can be divided into two types: those that interact and return to the periodic wave background and those that interact and return to the constant background. We extend our analysis method to analyze more complex solutions for multidimensional nonlocal integrable systems. [ABSTRACT FROM AUTHOR]