Dmitry E. Pelinovsky and Catherine Sulem (Department of Mathematics, University of Toronto)
Spectral decomposition for the Dirac system
associated to the DSII equation
(59K, LaTeX)
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.