Kedziora David J, Ankiewicz Adrian, Akhmediev Nail
Research School of Physics and Engineering, The Australian National University, Canberra, ACT, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056611. doi: 10.1103/PhysRevE.84.056611. Epub 2011 Nov 28.
Using the Darboux transformation technique and numerical simulations, we study the hierarchy of rational solutions of the nonlinear Schrödinger equation that can be considered as higher order rogue waves in this model. This analysis reveals the existence of rogue wave clusters with a high level of symmetry in the (x,t) plane. These structures arise naturally when the shifts in the Darboux scheme are taken to be eigenvalue dependent. We have found single-shell structures where a central higher order rogue wave is surrounded by a ring of first order peaks on the (x,t) plane.
