6 papers
Approximate direct and inverse scattering for the AKNS system
Vladislav V. Kravchenko
We study the direct and inverse scattering problems for the AKNS (Ablowitz-Kaup-Newell-Segur) system. New representations for the Jost solutions are obtained in the form of the pow…
Oleg Marichev: On the occasion of the eightieth anniversary
S. N. Askhabov, V. Kiryakova, V. V. Kravchenko +6
September 7, 2025 marked the 80th anniversary of the birth of Oleg Marichev. Marichev is known mathematician which has developed many of Mathematica's algorithms for the calculatio…
Implementation of the inverse scattering transform method for the nonlinear Schrödinger equation
Vladislav V. Kravchenko
We study the initial-value problem for the nonlinear Schrödinger equation. Application of the inverse scattering transform method involves solving direct and inverse scattering pr…
Neumann series of Bessel functions in direct and inverse spherically symmetric transmission eigenvalue problems
Vladislav V. Kravchenko, L. Estefania Murcia-Lozano, Nikolaos Pallikarakis
The transmission eigenvalue problem (TEP) plays a central role in inverse scattering theory. Despite substantial theoretical progress, the numerical solution of direct and inverse…
Reconstruction techniques for inverse Sturm-Liouville problems with complex coefficients
Vladislav V. Kravchenko
A variety of inverse Sturm-Liouville problems is considered, including the two-spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as…
Spectral parameter power series for Zakharov-Shabat direct and inverse scattering problems
Vladislav V. Kravchenko
We study the direct and inverse scattering problems for the Zakharov-Shabat system. Representations for the Jost solutions are obtained in the form of the power series in terms of…