Abstract
The spectral properties of the most general time-dependent potentials of the soliton type described by a self-adjoint operator acting in Hilbert space are discussed. The spectral decomposition for these potentials and the quasispectral decomposition for the Darboux transformation operators are obtained. The coherent states of such systems are examined. Finally, the measure realizing the decomposition of the identity operator in the projectors on the coherent states is calculated.
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