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A study of general rogue waves in some integrable reverse time nonlocalnonlinear equations is presented. Specifically, the reverse time nonlocalnonlinear Schr\"odinger (NLS) and nonlocal Davey-Stewartson (DS) equations areinvestigated, which are nonlocal reductions from the AKNS hierarchy. By usingDarboux transformation (DT) method, several types of rogue waves areconstructed. Especially, a unified binary DT is found for this nonlocal DSsystem, thus the solution formulas for nonlocal DSI and DSII equation can bewritten in an uniform expression. Dynamics of these rogue waves is separatelyexplored. It is shown that the (1+1)-dimensional rogue waves in nonlocal NLSequation can be bounded for both x and t, or develop collapsing singularities.It is also shown that the (1+2)-dimensional line rogue waves in the nonlocal DSequations can be bounded for all space and time, or have finite-timeblowing-ups. All these types depend on the values of free parameters introducedin the solution. In addition, the dynamics patterns in the multi- andhigher-order rogue waves exhibits more richer structures, most of which have nocounterparts in the corresponding local nonlinear equations.

General rogue waves and their dynamics in several reverse time integrable nonlocal nonlinear equations