An inverse scattering problem for eigenparameter-dependent discrete Dirac system with Levinson formula

Abstract

In this paper, we have considered an inverse scattering problem for discrete Dirac operator L with eigenparameter dependent boundary condition. At the outset, the Jost solution and the Jost function of L are given. Then the zeros of the Jost function and some properties of the scattering function are examined. After finding the scattering dataset and the main equation for the operator L, the uniqueness of the kernel, continuity of the scattering function and the appropriate Levinson type formula are obtained.

Keywords:

• Discrete Dirac equation
• eigenparameter
• scattering function
• Levinson formula

AMS Subject Classifications:

• 34L25
• 34L40
• 39A70
• 47A40
• 81U40

View correction statement:

Correction

Acknowledgments

The authors are grateful to the Mohapatra Family Foundation, the College of Graduate Studies of the University of Central Florida (UCF) for the postdoctoral fellowship, and the Department of Mathematics of the Kastamonu University for is support to pursue research work in Discrete Dirac Equations at UCF.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article was originally published with errors, which have now been corrected in the online version. Please see Correction 10.1080/17476933.2023.2250594

Additional information

Funding

This work was supported by Mohapatra Family Foundation (Grant award number: 00001642), and the College of Graduate Studies of the University of Central Florida (UCF) (Grant award number: 19100003).