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Scattering and inverse scattering for the AKNS system: A rational function approach
Author(s) -
Trogdon Thomas
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12434
Subject(s) - inverse scattering transform , inverse scattering problem , scattering , mathematics , rational function , mathematical analysis , operator (biology) , scattering theory , function (biology) , cauchy distribution , inverse , inverse problem , geometry , physics , quantum mechanics , biochemistry , chemistry , repressor , evolutionary biology , biology , transcription factor , gene
We consider the use of rational basis functions to compute the scattering and inverse scattering transforms associated with the AKNS (Ablowitz–Kaup–Newell–Segur) 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 Schrödinger operator with a sech 2 potential.