Inverse scattering problem for Sturm-Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition

Abstract

The inverse problem of the scattering theory for Sturm-Liouville operator on the half line with boundary condition depending quadratic on the spectral parameter is considered. Scattering data are defined, some properties of the scattering data are examined, the main equation is obtained, solvability of the integral equation is proved and uniqueness of algorithm to the potential with given scattering data is studied.

Pozitif Yarı Eksende Süreksizlik Koşuluna Sahip Sturm-Liouville Operatörünün Ters Saçılma Problemi

“…In case of the Sturm-Liouville equation with discontinuity conditions (or transmission conditions) at a point on the positive half line, the direct and inverse scattering problem with various boundary conditions and discontinuity conditions were investigated in (Huseynov and Osmanova, 2007;Huseynov and Osmanli, 2009;Huseynov and Mammadova, 2013;Manafov and Kablan, 2013). Moreover, the direct and inverse scattering problem for Sturm-Liouville operator with nonlinear spectral parameter in the boundary conditions were studied in (Goktas and Mamedov, 2020;Mamedov, 2009;Mamedov and Kosar, 2010;Mamedov and Kosar, 2011).…”

Continuity of the scattering function and Levinson‐type formula of Klein–Gordon equation

“…The inverse problem of scattering theory for a boundary value problem of – was defined the scattering data, the continuity of the scattering function was proved, and in a special case, the relation for the difference of the logarithm of the scattering function, which is called the Levinson‐type formula, was obtained .…”