Spectral decomposition for the Dirac system associated to the DSII equation

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.

References in corpus (1)

• Darboux Transformation for Dirac Equations with (1+1) potentials

Cited by in corpus (4)

• Numerical Study of Blowup in the Davey-Stewartson System
• Global Well-Posedness and Long-time Asymptotics for the Defocussing Davey-Stewartson II Equation in $H^{1,1}(R^2)$
• Soliton Solutions and their (In)stability for the Focusing Davey-Stewartson II Equation
• Boundary Value Problems for Linear PDEs with Variable Coefficients