The inverse nodal problem for the Sturm–Liouville operator L(q,a) arisen from acoustic scattering problems was considered. The authors showed that q(x) on the interval [0,1] can be uniquely determined by the interior twin-dense nodal subset W_T([0,1]), or W_T([a_0,1]), respectively. Using the above results, two uniqueness theorems of the spherically symmetric speed of sound η(r) for acoustic scattering problems are obtained.
Relation:
Journal of Inverse and Ill-posed Problems 25(2), p.237–249
