Effects of higher-order dispersion on envelope solitons
- 1 May 1990
- journal article
- Published by AIP Publishing in Physics of Fluids B: Plasma Physics
- Vol. 2 (5) , 889-900
- https://doi.org/10.1063/1.859288
Abstract
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.Keywords
This publication has 15 references indexed in Scilit:
- Soliton at the zero-group-dispersion wavelength of a single-model fiberOptics Letters, 1987
- Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibersOptics Letters, 1986
- Nonlinear pulse distortion in single-mode optical fibers at the zero-dispersion wavelengthPhysical Review A, 1986
- Soliton experiments in plasmasPlasma Physics, 1983
- Perturbations of Solitons and Solitary WavesStudies in Applied Mathematics, 1981
- Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theoryProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- A New Light Boson?Physical Review Letters, 1978
- Solitons under perturbationsPhysical Review A, 1977
- On an asymptotic solution of the Korteweg–de Vries equation with slowly varying coefficientsJournal of Fluid Mechanics, 1973
- Applications of Slowly Varying Nonlinear Dispersive Wave TheoriesStudies in Applied Mathematics, 1971