Potential splitting and numerical solution of the inverse scattering problem on the line. (English summary) Math. Methods Appl. Sci. 25 (2002), no. 4, 347–355. Summary: “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.