  Our analysis suggests strongly that stationary pulses exist in nonlinear
media with second-, third-, and fourth-order dispersion. A theory, based on the
variational approach, is developed for finding approximate parameters of such
solitons. It is obtained that the soliton velocity in the retarded reference
frame can be different from the inverse of the group velocity of linear waves.
It is shown that the interaction of the pulse spectrum with that of linear
waves can affect the existence of stationary solitons. These theoretical
results are supported by numerical simulations. Transformations between
solitons of different systems are derived. A generalization for solitons in
media with the highest even-order dispersion is suggested.
