Abstract

The nonlinear Schrödinger equation, describing the dynamical evolution of an optical pulse under the influence of linear (anomalous) dispersion or diffraction and nonlinear self-phase modulation can be taken in the form: where q(t) represents the form of the initially launched pulse. A key role in the inverse scattering scheme for solving the nonlinear Schrödinger is played by the concomitant Zakharov-Shabat scattering problem, [1]: where v₁ and v₂ are the Jost functions, which satisfy the asymptotic relations: v₁ → exp(–iζt) and v₂ → 0 as t → –∞.

© 1996 Optical Society of America