Multidimensional Analogues of Gelfand–Levitan, Marchenko and Krein Equations. Theory, Numerics and Applications

Аннотация

We consider the method of regularization of two dimensional (2D) inverse coefficient
problems based on the projection method and the approach of I.M. Gelfand, B.M. Levitan, M.G.
Krein and V.A. Marchenko. We propose a method of reconstruction of the potential, density and
velocity in 2D inverse coefficient problems. The 2D analogies of the I.M. Gelfand, B.M. Levitan and
M.G. Krein method are established. The 2D analog of the V.A. Marchenko equation is considered
for the Kadomtsev-Petviashvili equation. This approach can be easily applied to corresponding
multidimensional inverse problems. The results of numerical calculations are presented.