Effects of higher-order dispersion on envelope solitons.

The soliton modifications resulting from the addition of a small third derivative term, due to higher-order dispersion, to the nonlinear Schrödinger equation are investigated. Based on direct perturbation theory, it is shown that through first order, the soliton phase and velocity are modified, but the shape, amplitude, and width are unchanged. The radiation stimulated by the third derivative term, which is not predicted by the perturbation theory, is also derived. The expression obtained confirms the result of Wai (Ph.D. thesis, University of Maryland, 1988), which was obtained by a different method. The rate of change of the soliton amplitude due to this radiation, which emerges in front of the soliton, is calculated. The nonlinear term that drives the radiation is shown to grow to a value that is much larger than the unperturbed value. [ABSTRACT FROM AUTHOR]