Spatial growth rate of modulational instability in repulsive two-component Bose-Einstein condensates*

The onset of modulational instability (MI) in nonlinear fluids can give rise to various hydrodynamic phenomena, ranging from solitonic rogue waves to generalized turbulence, appearing in diverse contexts such as shallow water waves, nonlinear optics, and quantum fluids. In this work, we present experimental data and employ an analytical approach to characterize the rate of MI expansion in an immiscible two-component Bose-Einstein condensate with a hard-wall boundary. Through a combination of full 3D numerical simulations, an effective 1D model, and an analytical framework, we demonstrate strong agreement with experimental results, validating the analytical model in capturing the emergence of unstable dynamics.