Rogue waves in the nonlocal $${\mathcal {}}$$-symmetric nonlinear Schrödinger equation

Rogue waves in the nonlocal \({\mathcal {PT}}\)-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves show a much wider variety than those in the local NLS equation. For instance, the polynomial degrees of their denominators can be not only \(n(n+1)\), but also \(n(n-1)+1\) and \(n^2\), where n is an arbitrary positive integer. Dynamics of these rogue waves is also examined. It is shown that these rogue waves can be bounded for all space and time or develop collapsing singularities, depending on their types as well as values of their free parameters. In addition, the solution dynamics exhibits rich patterns, most of which have no counterparts in the local NLS equation.