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.
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