We study solitary wave solutions of the higher order nonlinear Schrödinger 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 -soliton solutions ( ) are determined; when these conditions are met the equation becomes the modified Korteweg–de Vries equation. A proper subset of these conditions meet the Painlevé plausibility conditions for integrability.
- Received 30 July 1996
- Published in the issue dated 20 January 1997
© 1997 The American Physical Society