Effects of higher-order dispersion on envelope solitons

Summary form only given, as follows. The effects of the third derivative term in the partial differential equation iu/sub t/+u/sub xx/+ mod u mod /sup 2/u-i epsilon u/sub xxx/=0 have been investigated. The use of a direct perturbation theory, in which u is expanded in powers of the perturbation parameter epsilon , yielded the following soliton modifications through order epsilon : the soliton retains its hyperbolic secant shape, but its velocity is increased and it experiences a negative wavenumber shift. No radiation is predicted by this direct perturbation theory. However, numerical integration of the equation showed that the soliton does radiate. An analysis of this radiation has shown that: (a) the soliton radiates energy at a constant rate proportional to exp(-const/ epsilon )/ epsilon ; (b) the radiated energy emerges as a plane wave in front of the soliton; and (c) the soliton loses an appreciable fraction of its energy in a time proportional to epsilon exp(const/ epsilon ). The analysis also shows that the Fourier transform of the radiation can be obtained from a third-order linear partial differential equation.<>