Zakharov-Shabat systems with single-hump and real, but not necessarily symmetric, potentials are shown to have purely imaginary eigenvalues only. Coupled with examples of double-hump potentials with nonimaginary eigenvalues, this establishes that confinement of Zakharov-Shabat eigenvalues to the imaginary axis is a characteristic of potentials whose energy is concentrated in a single region of the time axis.

• Received 9 August 2001

DOI:https://doi.org/10.1103/PhysRevE.65.036607