- Turkish Journal of Mathematics and Computer Science
- Vol: 14 Issue: 2
- Inverse Scattering Problem for the Sturm-Liouville Equation with Infinite Range of Discontinuous Con...
Inverse Scattering Problem for the Sturm-Liouville Equation with Infinite Range of Discontinuous Conditions
Authors : Rauf AMİROV, Selma GÜLYAZ ÖZYURT
Pages : 292-305
Doi:10.47000/tjmcs.1136596
View : 6 | Download : 15
Publication Date : 2022-12-30
Article Type : Research
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.Keywords : Impulse conditions, inverse problem, kernel, integral equation