  Spatial solitary waves in colloidal suspensions of spherical dielectric
nanoparticles are considered. The interaction of the nanoparticles is modelled
as a hard-sphere gas, with the Carnahan-Starling formula used for the gas
compressibility. Semi-analytical solutions, for both one and two spatial
dimensions, are derived using an averaged Lagrangian and suitable trial
functions for the solitary waves. Power versus propagation constant curves and
neutral stability curves are obtained for both cases, which illustrate that
multiple solution branches occur for both the one and two dimensional
geometries. For the one-dimensional case it is found that three solution
branches (with a bistable regime) occur, while for the two-dimensional case two
solution branches (with a single stable branch) occur in the limit of low
background packing fractions. For high background packing fractions the power
versus propagation constant curves are monotonic and the solitary waves stable
for all parameter values. Comparisons are made between the semi-analytical and
numerical solutions, with excellent comparison obtained.
