### 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.

Original language | English (US) |
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Article number | 132126 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 400 |

DOIs | |

State | Published - Dec 15 2019 |

### Keywords

- 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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## Cite this

Klein, C., McLaughlin, K., & Stoilov, N. (2019). Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation.

*Physica D: Nonlinear Phenomena*,*400*, [132126]. https://doi.org/10.1016/j.physd.2019.05.006