  Single-particle momentum spectra for a dynamically evolving one-dimensional
Bose gas are analysed in the semi-classical wave limit. Representing one of the
simplest correlation functions these give information about possible universal
scaling behaviour. Motivated by the previously discovered connection between
(quasi-)topological field configurations, strong wave turbulence, and
nonthermal fixed points of quantum field dynamics, soliton formation is studied
with respect to the appearance of transient power-law spectra. A random-soliton
model is developed to describe the spectra analytically, and the analogies and
difference between the appearing power laws and those found in a field theory
approach to strong wave turbulence are discussed. The results open a view on
solitary wave dynamics from the point of view of critical phenomena far from
thermal equilibrium and on a possibility to study this dynamics in experiment
without the necessity of detecting solitons in situ.
