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arXiv · 1809.08282

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

C. Klein·K. McLaughlin·N. Stoilov
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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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BibTeXRIS

C. Klein, K. McLaughlin, N. Stoilov. 2018-09-19. Spectral approach to the scattering map for the semi-classical defocusing Davey-Stewartson II equation. https://doi.org/10.1016/j.physd.2019.05.006

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