Mean-Frequency Shift of the Envelope Solitons in Media with Cubic Relaxing Nonlinearities

We study the mean-frequency variation of the envelope solitons propagating in nonlinear media with relaxing cubic nonlinearities. It is shown that the mean frequency in the propagation cannot only decrease in the case of the positive nonlinearity coefficient, which was previously known, but also increase in the case of the negative nonlinearity coefficient, which is observed for the gravity waves on a liquid surface.