# Transverse instability and disintegration of domain wall of relative phase in coherently coupled two-component Bose-Einstein condensates

## TL;DR

This paper analyzes the stability and disintegration of domain walls in two-component Bose-Einstein condensates with Rabi coupling, providing an analytical phase diagram and numerical simulations of instability evolution.

## Contribution

It presents the first analytical stability phase diagram for domain walls in coupled BECs and demonstrates nonlinear evolution of transverse instabilities through simulations.

## Key findings

- Identified the stability region in the Rabi frequency and coupling constant plane.
- Showed the domain wall's transverse instability outside the stable region.
- Numerically demonstrated the nonlinear evolution of the instability.

## Abstract

We study transverse instability and disintegration dynamics of a domain wall of a relative phase in two-component Bose-Einstein condensates with a coherent Rabi coupling. We obtain analytically the stability phase diagram of the stationary solution of the domain wall for the one-dimensional coupled Gross-Pitaevskii equations in the plane of the Rabi frequency and the intercomponent coupling constant. Outside the stable region, the domain wall is dynamically unstable for the transverse modulation along the direction perpendicular to the phase kink. The nonlinear evolution associated with the instability is demonstrated through numerical simulations for both the domain wall without edges and that with edges formed by the quantized vortices.