Optical Solitary Waves in the Higher Order Nonlinear Schrödinger Equation

Phys. Rev. Lett. 78, 448 – Published 20 January 1997
M. Gedalin, T. C. Scott, and Y. B. Band

Abstract

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 N-soliton solutions ( N2) 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.

DOI: http://dx.doi.org/10.1103/PhysRevLett.78.448

  • Received 30 July 1996
  • Published in the issue dated 20 January 1997

© 1997 The American Physical Society

Authors & Affiliations

M. Gedalin, T. C. Scott, and Y. B. Band

  • Departments of Chemistry and Physics, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel

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