Optical Solitary Waves in the Higher Order Nonlinear Schrodinger Equation
patt-sol
2009-10-30 v1 Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
solv-int
Abstract
We study solitary wave solutions of the higher order nonlinear Schrodinger equation for the propagation of short light pulses in an optical fiber. Using a scaling transformation we reduce the equation to a two-parameter canonical form. Solitary wave (1-soliton) solutions exist provided easily met inequality constraints on the parameters in the equation are satisfied. Conditions for the existence of N-soliton solutions (N>1) are determined; when these conditions are met the equation becomes the modified KdV equation. A proper subset of these conditions meet the Painleve plausibility conditions for integrability.
Keywords
Cite
@article{arxiv.patt-sol/9612004,
title = {Optical Solitary Waves in the Higher Order Nonlinear Schrodinger Equation},
author = {M. Gedalin and T. C. Scott and Y. B. Band},
journal= {arXiv preprint arXiv:patt-sol/9612004},
year = {2009}
}
Comments
REVTeX, 4 pages, no figures. To appear in Phys. Rev. Lett