The inverse scattering transform (IST) is developed for a class of matrix nonlinear Schrödinger‐type systems whose reductions include two equations that model certain hyperfine spin
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
 Award ID(s):
 1945652
 NSFPAR ID:
 10448189
 Publisher / Repository:
 WileyBlackwell
 Date Published:
 Journal Name:
 Studies in Applied Mathematics
 Volume:
 147
 Issue:
 4
 ISSN:
 00222526
 Page Range / eLocation ID:
 p. 14431480
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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