title: Triangular rogue wave cascades.
abstract: By numerically applying the recursive Darboux transformation technique, we study high-order rational solutions of the nonlinear Schrödinger equation that appear spatiotemporally as triangular arrays of Peregrine solitons. These can be considered as rogue wave cascades and complement previously discovered circular cluster forms. In this analysis, we reveal a general parametric restriction for their existence and investigate the interplay between cascade and cluster forms. As a result, we demonstrate how to generate many more hybrid rogue wave solutions, including semicircular clusters that resemble claws.
authors.affiliation: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia. djk105@rsphysse.anu.edu.au
authors.forename: David J
authors.initials: DJ
authors.lastname: Kedziora
authors.forename: Adrian
authors.initials: A
authors.lastname: Ankiewicz
authors.forename: Nail
authors.initials: N
authors.lastname: Akhmediev
mesh_terms: D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011789:Quantum Theory; D012212:Rheology / Q000379:methods*