Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential
A method for solving the integral Gelfand – Levitan – Marchenko (GLM) equation for the Sturm – Liouville operator with a step-type potential is obtained. The scattering function is found explicitly. An associated system of infinite recurrence equations is solved. The integral operator kernel is pre...
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Datum: | 2003 |
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1. Verfasser: | |
Format: | Artikel |
Sprache: | English |
Veröffentlicht: |
Інститут математики НАН України
2003
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Schriftenreihe: | Нелінійні коливання |
Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/176153 |
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Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
Zitieren: | Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential / V.P. Revenko // Нелінійні коливання. — 2003. — Т. 6, № 1. — С. 74-82. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of UkraineZusammenfassung: | A method for solving the integral Gelfand – Levitan – Marchenko (GLM) equation for the Sturm – Liouville operator with a step-type potential is obtained. The scattering function is found explicitly. An associated
system of infinite recurrence equations is solved. The integral operator kernel is presented in an exact form
using Bessel function. A series of new integral representations for Bessel functions is obtained for the first
time. |
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