Uniqueness of Solution of the Inverse Problem of Scattering Theory for a Fourth Order Differential Bundle with Multiple Characteristics

Abstract

The system of four equations of Marchenko type allowing to restore the bundle by the scattering matrix is derived for a fourth order di®erential bundle in L₂ (0;+∞) in the case of multiple ±i roots of the main characteristic polynomial. The uniqueness of solution of the inverse problem is proved when the bundle has a pure continuous spectrum.