Recovery of the nearest potential field from the \(m\) observed eigenvalues
In this work, authors consider a new class of inverse problems. An approach to a complete solution to such a problem is developed. Within the framework of this approach, they consider a model problem of recovering the potential field \(\hat{V}\) from \(m\) observed eigenvalues of the Schrödinger operator, provided that such potential field is at the minimum distance from a priori given potential \(V_{a}\). In the main result, they establish a new type of relationship between the linear spectral problems and systems of nonlinear differential equations which enables us to find a solution to the inverse optimal spectral problem and obtain novel results on the existence of solutions to nonlinear problems as well.
scientific article; zbMATH DE number 7477787
scientific article