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• W3136223882 abstract "We consider the use of rational basis functions to compute the scattering and inverse scattering transforms associated with the AKNS system. The proposed numerical forward scattering transform computes the solution of the AKNS system that is valid on the entire real axis and thereby computes a reflection coefficient at a point by solving a single linear system. The proposed numerical inverse scattering transform makes use of a novel improvement in the rational function approach to the oscillatory Cauchy operator, enabling the efficient solution of certain Riemann--Hilbert problems without contour deformations. The latter development enables access to high-precision computations and this is demonstrated on the inverse scattering transform for the one-dimensional Schrodinger operator with a $mathrm{sech}^2$ potential." @default.
• W3136223882 created "2021-03-29" @default.
• W3136223882 creator A5038993211 @default.
• W3136223882 date "2021-03-17" @default.
• W3136223882 modified "2023-09-27" @default.
• W3136223882 title "Scattering and inverse scattering for the AKNS system: A rational function approach" @default.
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• W3136223882 hasPublicationYear "2021" @default.
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