Kompleks potansiyele sahip Sturm-Liouville operatörü için ters saçılma problemi ve bazı uygulamaları
On inverse scattering problem for the Sturm-Liouville operator with complex potential and some applications
- Tez No: 200523
- Danışmanlar: PROF.DR. BİLENDER PAŞAOĞLU
- Tez Türü: Yüksek Lisans
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Korteweg-de Vries equation, on inverse scattering problem, Sturm- Liouville operator, eigenfunction
- Yıl: 2007
- Dil: Türkçe
- Üniversite: Süleyman Demirel Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 63
Özet
Tez çalısmasında 0
Özet (Çeviri)
In this thesis, inverse scattering problem for which the Sturm-Liouville equation y p x y y 2 ? ' '+ ( ) = l (I) that is generated by the boundary condition ' (0) ( ) (0) 0 y ? a + il + l2 y = (II) with spectral parameter having ( ) (0, ) 2 p x Î L ¥ potential which is a complex variable function, is studied on the 0 < x < ¥ half-plane. On inverse scattering problems are forming a new method for solving the mathematical physics. In the first part of the thesis, it is given the abstract of the formation and progress of the various inverse problems. In the second part of the thesis, fundamental definitions and theorems that are related to the topic are explained. In the third part, the Sturm-Liouville equation, which has the nonlinear potential and integral indicators for the linear dependent solutions that enable the condition, which is given in the infinity of this equation and getting the asymptotic equations are explained. The spectral properties of the problem (I)-(II) are observed and according to these properties, method of finding the p(x) potential is studied in the fourth part. Also, method of finding exact solutions of the fundamental integral equation system obtained by specific condition of scattering data are given and according to these solutions, p(x) potential is determined. In the fifth part, as a practice of the results of previous parts, Cauchy problem is given for the KdV equation and the method of finding the exact solution, by making use of the inverse scattering problem for the Sturm-Liouville equation, is explained.
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