Experimentally Tractable Generation of High-Order Rogue Waves in Bose-Einstein Condensates

TL;DR

This paper presents a practical method for generating high-order rogue waves in Bose-Einstein condensates, demonstrating controllable extreme focusing events in one, two, and three dimensions, advancing experimental capabilities in nonlinear wave phenomena.

Contribution

It introduces an experimentally feasible scheme to produce high-order rogue waves in Bose-Einstein condensates across multiple dimensions, overcoming previous limitations of focusing nonlinear Schrödinger equations.

Findings

Numerical evidence of high-order rogue wave generation in 1D BECs.

Extension of rogue wave generation scheme to 2D and 3D settings.

Demonstration of second-order rogue waves despite finite-time blow-up constraints.

Abstract

In this work, we study a prototypical, experimentally accessible scenario that enables the systematic generation of so-called high-order rogue waves in atomic Bose-Einstein condensates. These waveforms lead to significantly and controllably more extreme focusing events than the famous Peregrine soliton. In one spatial dimension, we showcase conclusive numerical evidence that our scheme generates the focusing behavior associated with the first four rogue waves from the relevant hierarchy. We then extend considerations to anisotropic two-dimensional and even three-dimensional settings, establishing that the scheme can generate second order rogue waves despite the well-known limitation of finite-time blow up of focusing nonlinear Schr\"odinger equations.