What is it about?
We study solitary wave solutions of the higher order nonlinear Schrodinger equation (HONSE) 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.
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Why is it important?
If we consider the propagation of shorter (temporal) light pulses or over a longer distance, we need to consider higher-order corrections and therefore the pulse carrier envelope is governed by the higher-order nonlinear Schrödinger equation (HONSE) for which this paper provided a specialized (analytical) soliton solution.
Perspectives
This paper has been seminal and accumulated hundreds of citations for other soliton solutions to HONSE and other partial differential equations.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: Optical Solitary Waves in the Higher Order Nonlinear Schrödinger Equation, Physical Review Letters, January 1997, American Physical Society (APS),
DOI: 10.1103/physrevlett.78.448.
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