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

Christian Klein, Kenneth D T Mclaughlin, Nikola Stoilov

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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.

Original languageEnglish (US)
Article number132126
JournalPhysica D: Nonlinear Phenomena
Publication statusPublished - Jan 1 2019



  • D-bar problems
  • Davey–Stewartson equations
  • Fourier spectral method

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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