Potential Splitting and Numerical Solution of the Inverse Scattering Problem on the Line
نویسندگان
چکیده
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. PACS Numbers (1999): 02.60.Lj, 03.65.Nk Mathematics Subject Classification (2000): 34L25, 34L40, 35Q53, 47A40, 65L09, 81U05, 81U40
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