Premium
Potential splitting and numerical solution of the inverse scattering problem on the line
Author(s) -
Aktosun Tuncay,
Sacks Paul E.
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.292
Subject(s) - mathematics , reflection (computer programming) , integrable system , inverse scattering problem , inverse problem , line (geometry) , mathematical analysis , initial value problem , moment (physics) , korteweg–de vries equation , scattering , numerical analysis , inverse , geometry , classical mechanics , quantum mechanics , physics , nonlinear system , computer science , programming language
The one‐dimensional Schrödinger equation is considered when the potential is real valued, integrable, has a finite first moment, and contains no bound states. From either of the two reflection coefficients of such a potential the right and left reflection coefficients are extracted corresponding to the left and right halves of the potential, respectively, and such half‐line potentials are readily constructed from the extracted reflection coefficients. A computational procedure is described for such extractions and the construction of the two halves of the potential, and some applications are considered such as a numerical solution of the initial value problem for the Korteweg–de Vries equation. The theory is illustrated with some explicit examples. Copyright © 2002 John Wiley & Sons, Ltd.