  Soliton solutions are studied for paraxial wave propagation with
intensity-dependent dispersion. Although the corresponding Lagrangian density
has a singularity, analytical solutions, derived by the pseudo-potential method
and the corresponding phase diagram, exhibit one- and two-humped solitons with
almost perfect agreement to numerical solutions. The results obtained in this
work reveal a hitherto unexplored area of soliton physics associated with
nonlinear corrections to wave dispersion.
