  We fill some of existed gaps in the correspondence between Supersymmetric
Quantum Mechanics and the Inverse Scattering Transform by extending the
consideration to the case of paired stationary and non-stationary Hamiltonians.
We formulate the corresponding to the case Goursat problem and explicitly
construct the kernel of the non-local Inverse Scattering Transform, which
solves it. As a result, we find the way of constructing non-hermitian
Hamiltonians from the initially hermitian ones, that leads, in the case of
real-valued spectra of both potentials, to pairing of ${\cal CPT/PT}$-invariant
Hamiltonians. The relevance of our proposal to Quantum Optics and optical
waveguides technology, as well as to non-linear dynamics and Black Hole Physics
is briefly discussed.
