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Weyl theory for a non-classical system depending rationally on the spectralparameter is treated. Borg-Marchenko-type uniqueness theorem is proved. Thesolution of the inverse problem is constructed. An application to sine-Gordonequation in laboratory coordinates is given.

integral equations and operator theory

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