Generic quartic solitons in optical media

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.