In this article the scattering matrix pertaining to the defocusing matrix Zakharov-Shabat system on the line is related to the scattering operator arising from time-dependent scattering theory. Further, the scattering data allowing for a unique retrieval of the potential in the defocusing matrix Zakharov-Shabat system are characterized. Mathematics Subject Classification (2000). Primary 34A55, ...

The one-dimensional matrix Schrr odinger equation is considered when the matrix potential is selfadjoint and satisses certain general restrictions. The small-energy asymptotics of the scattering solutions and scattering coeecients are derived. The continuity of the scattering coeecients is established. The unique solvability of the corresponding matrix Marchenko integral equations is proved. Sh...

In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets and associated Weyl functions for (in general nondensely defined) symmetric operators is applied. Th...

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...

Scattering theory is the analysis of the motion of several interacting particles. Inverse problems in scattering theory seek the answer to the question: can one determine the interactions between particles by a scattering experiment, so, for instance, does the scattering matrix, or a part of the scattering matrix, determine the interaction? The answer, and the difficulty, greatly depends on the...