  We find exact solutions to nonlinear Schr\"odinger equation in the presence
of self-steepening and self-frequency shift. These include periodic solutions
and localized solutions of dark-bright type which can be {\emph{chiral}}, and
chirality being controlled by sign of self steepening term. A new form of self
phase modulation, which can be tuned by higher order nonlinearities as also by
the initial conditions, distinct from nonlinear Schr\"odinger equation,
characterizes these solutions. In certain nontrivial parameter domain solutions
are found to satisfy {\emph{linear}} Schr\"odinger equation, indicating
possiblity of linear superposition in this nonlinear system. Dark and bright
solitons exist in both anomalous and normal dispersion regimes and a duality
between dark-bright type of solution and kinematic-higher order chirping is
also seen. Localized kink solutions similar to NLSE solitons, but with very
different self phase modulation, are identified.
