Spectral decomposition for the Dirac system associated to the DSII equation

A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Davey-Stewartson II (DSII) equation. The discrete spectrum in the spectral problem corresponds to eigenvalues em bedded into a two-dimensional essential spectrum. We show that these embedd ed eigenvalues are structurally unstable under small variations of the init ial data. This instability leads to the decay of localized initial data int o continuous wavepackets prescribed by the nonlinear dynamics of the DSII e quation.