Vector rogue waves in spin-1 Bose-Einstein condensates with spin-orbit coupling

TL;DR

This paper investigates three-component rogue waves in spin-1 Bose-Einstein condensates with spin-orbit coupling, providing analytical solutions and numerical validation, revealing their shapes, velocities, and conditions for existence.

Contribution

It introduces approximate analytical solutions for rogue waves in spin-1 BECs with SOC, including higher-order and striped shapes, and explores their existence domains via modulational instability.

Findings

Analytical rogue wave solutions match numerical simulations.

Rogue waves exhibit different velocities across components due to SOC.

Existence of rogue waves is linked to baseband modulational instability.

Abstract

We analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose-Einstein condensates with Raman-induced spin-orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions for RWs with positive and negative effective masses, determined by the effective dispersion of the system. The solutions include RWs with smooth and striped shapes, as well as higher-order RWs. The analytical solutions demonstrate that the RWs in the three components of the system exhibit different velocities and their maximum peaks appear at the same spatiotemporal position, which is caused by SOC and interactions. The accuracy of the approximate analytical solutions is corroborated by comparison with direct numerical simulations of the underlying system. Additionally, we systematically explore existence domains for the RWs determined by the baseband modulational instability (BMI). Numerical simulations corroborate that, under the action of BMI, plane waves with random initial perturbations excite RWs, as predicted by the approximate analytical solutions.