D.E. Pelinovsky and C. Sulem
Spectral Decomposition for the Dirac System Associated
to the DSII Equation
Inverse Problems 16, 59-74 (2000)
Abstract:
A new (scalar) spectral decomposition is found for the Dirac
system in two dimensions associated to the focusing
Davey-Stewartson II (DSII) equation. Discrete spectrum in
the spectral problem corresponds to eigenvalues embedded
into a two-dimensional essential spectrum. We show that
these embedded eigenvalues are structurally unstable under
small variations of the initial data. This instability leads
to the decay of localized initial data into continuous wave
packets prescribed by the nonlinear dynamics of the DSII
equation.