Kedziora David J, Ankiewicz Adrian, Akhmediev Nail
Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056602. doi: 10.1103/PhysRevE.86.056602. Epub 2012 Nov 8.
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.
通过数值应用递归达布变换技术，我们研究了非线性薛定谔方程的高阶有理解，这些解在时空上表现为佩雷格林孤子的三角阵列。这些可以被视为 rogue 波级联，并补充了先前发现的圆形簇形式。在该分析中，我们揭示了它们存在的一般参数限制，并研究了级联和簇形式之间的相互作用。结果，我们展示了如何生成更多的混合 rogue 波解，包括类似爪子的半圆形簇。
