  We study an intense-short pulse propagation in a saturable cubic-quintic
nonlinear media in the presence of nonlinear dispersion within the framework of
an extended variational approach. We derive an effective equation for the pulse
width and demonstrate how the saturation due to nonlinearity is achieved in
presence of nonlinear dispersion. We find that the nonlinear dispersion can
change the pulse width and induce motion in the system. The direction of
induced motion depends on the sign of nonlinear dispersion. The pulse is
energetically stable at an equilibrium width. A disturbance can, however,
induce oscillation in pulse width, the frequency of which is always smaller due
to nonlinear dispersion. We check dynamical stability by a direct numerical
simulation.
