Rogue wave patterns in the nonlinear Schrödinger equation

Rogue wave patterns in the nonlinear Schrödinger equation are analytically studied. It is shown that when an internal parameter rogue waves (which controls shape and phase of initial weak perturbations to uniform background) large, these would exhibit clear geometric structures, which formed by Peregrine shapes such as triangle, pentagon, heptagon nonagon, with a possible lower-order at its center. These determined root structures Yablonskii–Vorob’ev polynomial hierarchy, their orientations controlled large parameter. also multiple parameters but satisfy certain constraints, similar still hold. Comparison between true our analytical predictions shows excellent agreement. • Schrodinger determined. A deep connection polynomials found. Analytical match ones perfectly.