Spectral approach to the scattering map for the semi-classical defocusing Davey-Stewartson II equation

Abstract

The inverse scattering approach for the defocusing Davey-Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We treat the D-bar problem as a complex linear second order integral equation which is solved with discrete Fourier transforms complemented by a regularization of the singular parts by explicit analytic computation. The resulting algebraic equation is solved either by fixed point iterations or GMRES. Several examples for small values of the semi-classical parameter in the system are discussed.

References in corpus (3)

• Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
• Global Well-Posedness and Long-time Asymptotics for the Defocussing Davey-Stewartson II Equation in $H^{1,1}(R^2)$
• A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davey-Stewartson Equation and to the Inverse Boundary Value Problem of Calderón

Cited by in corpus (3)

• High precision numerical approach for the Davey-Stewartson II equation for Schwartz class initial data
• Numerical scattering for the defocusing Davey-Stewartson II equation for initial data with compact support
• Numerical study of Davey-Stewartson I systems