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Potential splitting and numerical solution of the inverse scattering problem on the line

✍ Scribed by Tuncay Aktosun; Paul E. Sacks

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 100 KB
Volume: 25
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.292

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✦ Synopsis

Abstract

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.

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