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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.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02353053
Contributeur : Imb - Université de Bourgogne <>
Soumis le : jeudi 7 novembre 2019 - 10:37:34
Dernière modification le : jeudi 5 mars 2020 - 15:32:56

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Christian Klein, Ken Mclaughlin, Nikola Stoilov. Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation. Physica D: Nonlinear Phenomena, Elsevier, 2019, 400, pp.132126. ⟨10.1016/j.physd.2019.05.006⟩. ⟨hal-02353053⟩

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