  A modified Gross-Pitaevskii approximation was introduced recently for bosons
in dimension $d\le2$ by Kolomeisky {\it et al.} (Phys. Rev. Lett. {\bf 85} 1146
(2000)). We use the density functional approach with sixth-degree interaction
energy term in the Bose field to reproduce the stationary-frame results of
Kolomeisky {\it et al.} for a one-dimensional Bose-Einstein system with a
repulsive interaction. We also find a soliton solution for an attractive
interaction, which may be boosted to a finite velocity by a Galilean
transformation. The stability of such a soliton is discussed analytically. We
provide a general treatment of stationary solutions in one dimension which
includes the above solutions as special cases. This treatment leads to a
variety of stationary wave solutions for both attractive and repulsive
interactions.
