Abstract

Dark solitons are characterized by eigen-values that are determined from the initial conditions by using the so-called direct scattering method. This technique will be described, and several interesting cases will be discussed. In particular, for jump discontinuities, the problem simplifies to the ubiquitous quantum well problem. Level splitting of the eigenvalues occurs when two or more "wells" are brought together. Bands in the soliton spectrum occur when many identical wells exist. These results will be used to describe collisionless optical logic gates and other applications.

© 1992 Optical Society of America