  The term "direct scattering study" refers to the calculation and analysis of
the discrete eigenvalues of the associated Zakharov-Shabat (ZS) eigenvalue
problem. The direct scattering study was applied to time-dependent oscillating
solitons that arise as attractors in the parametrically driven nonlinear
Schr\"odinger equation. Four different types of attractors within the parameter
space are identified, each with a unique soliton content structure. These
structures include radiation-induced nonlinear modes and soliton complex
structures. The different types of attractors are used to characterise the
dependence of the attractors on damping and driving parameters. Period-doubling
bifurcations are shown to affect the radiation emissions of oscillating
solitons. The role of soliton complex structures and radiation in the formation
of spatio-temporal chaos is also identified.
