Construction of the solution of the inverse spectral problem for a system depending rationally on the spectral parameter, Borg-Marchenko-type theorem, and sine-Gordon equation

Abstract

Weyl theory for a non-classical system depending rationally on the spectral parameter is treated. Borg-Marchenko-type uniqueness theorem is proved. The solution of the inverse problem is constructed. An application to sine-Gordon equation in laboratory coordinates is given.