Abstract
An inverse scattering problem for a layered medium that supports N types of linear waves is considered, that is an 2N× 2N generalization of the Dirac type equation in one dimension. Both the direct and inverse scattering problems for this problem are studied. The relevant inverse problem is formulated to a uniquely solvable Riemann-Hilbert problem which can be transformed to a matrix singular integral equation. It is shown that the only contribution to reconstruction of potentials vanishing at infinity, comes from the solution which is normalized to identity matrix I at infinity. The remarkable difference from the conventional “regular” N× N first order linear spectral problem is that the problem considered here are of both the properties of the well-known 2× 2 Dirac type equation and the properties of the conventional “regular” N× N first order linear spectral problem.
