High-order Rogue Wave solutions for the Coupled Nonlinear Schr\"{o}dinger Equations-II

TL;DR

This paper derives high-order rogue wave solutions for two-component coupled nonlinear Schrödinger equations using generalized Darboux transformation, revealing complex distribution patterns and expanding understanding of rogue wave dynamics in various physical systems.

Contribution

It introduces a method to obtain high-order rogue wave solutions without wave vector restrictions, enhancing the analysis of rogue wave excitation in multi-component systems.

Findings

Distribution patterns of vector rogue waves are more diverse than scalar ones.

First and second-order rogue wave solutions are explicitly constructed.

Results apply to Bose-Einstein condensates, nonlinear fibers, and superfluids.

Abstract

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the special limitation on the wave vectors. As an application, we exhibit the first, second-order rogue wave solution and the superposition of them by computer plotting. We find the distribution patterns for vector rogue waves are much more abundant than the ones for scalar rogue waves, and also different from the ones obtained with the constrain conditions on background fields. The results further enrich and deep our realization on rogue wave excitation dynamics in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.