Reconstruction for the spherically symmetric speed of sound from nodal data

Abstract

In this article, we consider the inverse nodal problem for the Sturm–Liouville operator arisen from acoustic scattering problems. We show that a dense subset of nodal points can uniquely determine the potential on the finite interval [0, 1] and coefficient a of the boundary condition and provide a constructive procedure for the solution of the inverse nodal problem. A corollary of this theorem is to reconstruct the spherically symmetric speed of sound on the interval [0, b] for acoustic scattering problems from nodal data.

Keywords:

• inverse nodal problem
• Sturm–Liouville problem
• potential
• spherically symmetric speed of sound

AMS Subject Classifications::

• 34A55
• 34B24
• 47E05

Acknowledgements

The authors acknowledge helpful comments and valuable suggestions from the referees, which obviously have improved the quality of the original manuscript. This work was supported by the National Natural Science Foundation of China (No. 11171152) and the Natural Science Foundation of Jiangsu (No. BK 2010489).