Scattering and inverse scattering for the AKNS system: A rational function approach

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...

Full description

Saved in:
Bibliographic Details
Published in:Studies in applied mathematics (Cambridge) 2021-11, Vol.147 (4), p.1443-1480
Main Author: Trogdon, Thomas
Format: Article
Language:English
Subjects:
Basis functions
Cauchy integrals
Forward scattering
Inverse scattering
Mathematical analysis
Operators (mathematics)
rational approximation
Rational functions
Reflectance
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 sech2 potential.
ISSN:0022-2526
1467-9590
DOI:10.1111/sapm.12434