Purely imaginary eigenvalues of Zakharov-Shabat systems.
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.
Klaus
M
M
Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123, USA.
Shaw
J K
JK