  We study the dynamics of femtosecond light pulse propagation in a
cubic-quintic medium exhibiting dispersive effect up to the fourth order as
well as self-frequency shift and self-steepening nonlinearity. A rich variety
of periodic and solitary wave solutions are derived for the governing
generalized higher-order nonlinear Schr\"{o}dinger equation in the presence of
self-frequency shift and self-steepening effects. It is found that the
frequency shift, inverse velocity, amplitude and wave number of both periodic
and solitary waves depend on dispersion coefficients and nonlinearity
parameters as well. The conditions on optical fiber parameters for the
existence of these structures are presented. The stability of these periodic
and solitary wave solutions is studied numerically by adding white noise. It is
proved by using the numerical split-step Fourier method that the profile of
these nonlinear waves remains unchanged during evolution.
