  The dynamical evolution of spatial patterns in a complex system can reveal
the underlying structure and stability of stationary states. As a model system
we employ a two-component rubidium Bose-Einstein condensate at the transition
from miscible to immiscible with the additional control of linear
interconversion. Excellent agreement is found between the detailed experimental
time evolution and the corresponding numerical mean-field computations.
Analyzing the dynamics of the system, we find clear indications of stationary
states that we term nonlinear dressed states. A steady state bifurcation
analysis reveals a smooth connection of these states with dark-bright soliton
solutions of the integrable two-component Manakov model.
