Spectral decomposition for the Dirac system associated to the DSII equation

Details Spectral decomposition for the Dirac system associated to the DSII equation Spectral decomposition for the Dirac system associated to the DSII equation

1999-07-08

arxiv.org/abs/solv-int/9907011v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.1088/0266-5611/16/1/306

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.

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