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Journals / Turkish Journal of Mathematics and Computer Science / 2022 / Cilt: 14 - Sayı: 2

Inverse Scattering Problem for the Sturm-Liouville Equation with Infinite Range of Discontinuous Conditions

Rauf AMİROV
Selma GÜLYAZ ÖZYURT
Pages
292–305
Publication Date
2022-12-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, in the paper we prove uniqueness of the determination of the potential by the scattering data.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we construct the new integral representation of the Jost solution of Sturm-Liouville equation with impuls in the semi axis $[0,+\infty )$ and we give this type of relation, examine the properties of the Kernel function and their partial derivatives with $x$ and $\ t$, constructed integral representation and obtain the partial differential equation provided by this Kernel function.
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Key Findings & Data:In this paper, we construct the new integral representation of the Jost solution of Sturm-Liouville equation with impuls in the semi axis $[0,+\infty )$ and we give this type of relation, examine the properties of the Kernel function and their partial derivatives with $x$ and $\ t$, constructed integral representation and obtain the partial differential equation provided by this Kernel function.
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Conclusion & Impact:Finally, in the paper we prove uniqueness of the determination of the potential by the scattering data.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Impulse conditions · inverse problem · kernel

Abstract

In this paper, we construct the new integral representation of the Jost solution of Sturm-Liouville equation with impuls in the semi axis $[0,+\infty )$ and we give this type of relation, examine the properties of the Kernel function and their partial derivatives with $x$ and $\ t$, constructed integral representation and obtain the partial differential equation provided by this Kernel function. Finally, in the paper we prove uniqueness of the determination of the potential by the scattering data.

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Cite This Article

AMİROV, R., ÖZYURT, S. G. (2022). Inverse Scattering Problem for the Sturm-Liouville Equation with Infinite Range of Discontinuous Conditions. Turkish Journal of Mathematics and Computer Science, Cilt: 14 - Sayı: 2, 292–305. https://ajindex.com/articles/865179

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