Dynamics of rogue waves in the Davey-Stewartson II equation

TL;DR

This paper derives and analyzes rogue wave solutions in the Davey-Stewartson-II equation, revealing their formation, interaction, and potential for finite-time blow-up, thus advancing understanding of complex wave dynamics.

Contribution

It introduces determinant-based rogue wave solutions for the Davey-Stewartson-II equation, including fundamental, multi, and higher-order waves, and explores their dynamic behaviors and blow-up phenomena.

Findings

Fundamental rogue waves are line-shaped and revert to background.

Multi-rogue waves model interactions between fundamental waves.

Higher-order rogue waves can blow up in finite time under certain conditions.

Abstract

General rogue waves in the Davey-Stewartson-II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background in a line profile and then retreat back to the constant background again. It is also shown that multi-rogue waves describe the interaction between several fundamental rogue waves, and higher-order rogue waves exhibit different dynamics (such as rising from the constant background but not retreating back to it). A remarkable feature of these rogue waves is that under certain parameter conditions, these rogue waves can blow up to infinity in finite time at isolated spatial points, i.e., exploding rogue waves exist in the Davey-Stewartson-II equation.