Optical Solitary Waves in the Higher Order Nonlinear Schrödinger Equation
/ Authors
/ Abstract
We study solitary wave solutions of the higher order nonlinear Schr\"odinger 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 always exist provided easily met inequality constraints on the parameters in the equation are satisfied. Conditions for the existence of $N$-soliton solutions ( $N\ensuremath{\ge}2$) are determined; when these conditions are met the equation becomes the modified Korteweg\char21{}de Vries equation. A proper subset of these conditions meet the Painlev\'e plausibility conditions for integrability.
Journal: Physical Review Letters