52 citations · 535 across the 39 of their papers we have counts for
44 papers
Recovery of the matrix potential of the one-dimensional Dirac equation from spectral data
Emmanuel Roque, Sergii M. Torba
A method for solving an inverse spectral problem for the one-dimensional Dirac equation is developed. The method is based on the Gelfand-Levitan equation and the Fourier-Legendre s…
Recovery of the rod cross section shape
Vladislav V. Kravchenko, Sergii M. Torba, Alexander O. Vatulyan
A direct method for solving the inverse problem of determining the shape of the cross section of a rod is proposed. The method is based on Neumann series of Bessel functions repres…
Representation of solutions of the one-dimensional Dirac equation in terms of Neumann series of Bessel functions
Emmanuel Roque, Sergii M. Torba
A representation of solutions of the one-dimensional Dirac equation is obtained. The solutions are represented as Neumann series of Bessel functions. The representations are shown…
Spectral parameter power series representation for regular solutions of the radial Dirac system
Emmanuel Roque, Sergii M. Torba
A spectral parameter power series (SPPS) representation for the regular solution of the radial Dirac system with complex coefficients is obtained, as well as a SPPS representation…
Realization of the inverse scattering transform method for the Korteweg-de Vries equation
Sergei M. Grudsky, Vladislav V. Kravchenko, Sergii M. Torba
A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost sol…
A practical method for recovering Sturm-Liouville problems from the Weyl function
Vladislav V. Kravchenko, Sergii M. Torba
In the paper we propose a direct method for recovering the Sturm-Liouville potential from the Weyl-Titchmarsh -function given on a countable set of points. We show that using th…