Multidimensional Analogues of Gelfand–Levitan, Marchenko and Krein Equations. Theory, Numerics and Applications (Вестник КазНУ. Серия математика, механика, информатика, 2018)
We consider the method of regularization of two dimensional (2D) inverse coefficientproblems 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 andvelocity in 2D inverse coefficient problems. The 2D analogies of the I.M. Gelfand, B.M. Levitan andM.G. Krein method are established. The 2D analog of the V.A. Marchenko equation is consideredfor the Kadomtsev-Petviashvili equation. This approach can be easily applied to correspondingmultidimensional inverse problems. The results of numerical calculations are presented.
Keywords: Gelfand-Levitan equation; Krein equation; Marchenko equation; inverse coefficient problem; inverse scattering problem