Circular viewpoint of higher-order rogue wave structures of the nonlinear Schrödinger equation

Abstract We analyze rogue wave patterns for various orders of the nonlinear Schrödinger equation for large values of solution parameters. We use a combination of exact solutions, geometric constructions and polynomial approximations for analysis, and introduce a new way of viewing the formations of rogue waves, including the triangular ones, by showing that they all can be represented as occupying circular shells, some of which contain ‘nuclei’.