Prolongation structure for a nonlinear equation with explicit space dependence

Abstract

A nonlinear Schroedinger equation with a term depending explicitly on a space variable, e.g., iψt+ψxx+(−2αx+2‖E‖2) ψ=0 with ψ=Eeiφ has been treated in the language of differential forms and prolongation. The inverse scattering equations previously invented by Liu and Chen are obtained. A unique feature of the analysis is explicit space–time dependence of the pfaffian forms.