Inverse scattering problem on the half-axis for a first order system of ordinary differential equations

Mansur I. Ismailov

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arXiv · 1306.4770

Inverse scattering problem on the half-axis for a first order system of ordinary differential equations

Mansur I. Ismailov

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Abstract

In this article, the inverse scattering problem (ISP) of recovering the matrix coefficient of a first order system of ordinary differential equations on the half-axis from its scattering matrix is considered. In the case of a triangular structure of the matrix coefficient, this system has a Volterra-type integral transformation operator at infinity. Such type of transformation operator allows to determine the scattering matrix on the half-axis via the matrix Riemann-Hilbert factorization in the case, where contour is real axis, normalization is canonical and all the partial indices are zero. The ISP on the half-axis is solved by reducing it to ISP on the whole axis for the considered system with the coefficients that are extended to the whole axis as zero.

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BibTeX RIS

Mansur I. Ismailov. 2013-06-20. Inverse scattering problem on the half-axis for a first order system of ordinary differential equations. https://arxiv.org/abs/1306.4770

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