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
1. Verfasser: Revenko, V.P.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2003
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 Ukraine
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Zusammenfassung: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.