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 : 20 | Download : 21

Publication Date : 2022-12-30

Article Type : Research Paper

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