Inverse Scattering Problem for Sturm-Liouville Operator with Discontinuity Conditions on the Positive Half Line

Year 2021, Volume: 7 Issue: 3, 401 - 409, 31.12.2021

Özge Akçay

https://doi.org/10.29132/ijpas.908009

Abstract

In this paper, we consider the inverse scattering problem for Sturm-Liouville operator with discontinuity conditions at some point on the positive half line. The scattering data of this boundary value problem is examined. The resolvent operator is constructed and the expansion formula with respect to the eigenfunctions of this boundary value problem is obtained. The main equation or modified Marchenko equation of the inverse scattering problem is derived and an algorithm of the construction of the potential function according to scattering data of this boundary value problem is given.

Keywords

Sturm-Liouville equation, discontinuity conditions, inverse scattering problem, main equation

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

Abstract

Bu çalışmada, pozitif yarı eksen üzerindeki bir noktada süreksizlik koşuluna sahip Sturm-Liouville operatörünün ters saçılma problemi ele alınmıştır. Ele alınan sınır değer probleminin saçılma verileri incelenmiştir. Rezolvent operatörü inşa edilmiş ve sınır değer probleminin özfonksiyonlarına göre ayrışım formülü elde edilmiştir. Ters saçılma probleminin temel denklemi veya modifiye edilmiş Marchenko denklemi elde edilmiş ve sınır değer probleminin saçılma verilerine göre potansiyel fonksiyonun inşa edilme algoritması verilmiştir.

Keywords

Sturm-Liouville denklemi, süreksizlik koşulları, ters saçılma problemi, temel denklem

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