Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential

• Published in: Нелінійні коливання
• Date: 2003
• Main Author: Revenko, V.P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2003
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/176153
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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 kerne...