2021/03/17 by Thomas Trogdon, Trogdon, Thomas · 2 citations
Physics and Astronomy · #33F05 #34L16 #34L25 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Photorefractive and Nonlinear Optics #Quantum Mechanics and Non-Hermitian Physics #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2103.09953
openalex publication_date 2021/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the use of rational basis functions to compute the scattering and\ninverse scattering transforms associated with the AKNS system. The proposed\nnumerical forward scattering transform computes the solution of the AKNS system\nthat is valid on the entire real axis and thereby computes a reflection\ncoefficient at a point by solving a single linear system. The proposed\nnumerical inverse scattering transform makes use of a novel improvement in the\nrational function approach to the oscillatory Cauchy operator, enabling the\nefficient solution of certain Riemann--Hilbert problems without contour\ndeformations. The latter development enables access to high-precision\ncomputations and this is demonstrated on the inverse scattering transform for\nthe one-dimensional Schr "odinger operator with a \sech2 potential.\n