Soliton evolution and radiation loss for the nonlinear Schrödinger equation

William L. Kath*, Noel F. Smyth

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

132 Scopus citations

Abstract

The transient evolution of general initial pulses into solitons for the nonlinear Schrödinger (NLS) equation is considered. By employing a trial function which consists of a solitonlike pulse with variable parameters plus a linear dispersive term in an averaged Lagrangian, ordinary differential equations (ODE's) are derived which approximate this evolution. These approximate equations take into account the effect of the generated dispersive radiation upon the pulse evolution. Specifically, in the approximate ODE's the radiation acts as a damping which causes the pulse to decay to a steady soliton. The solutions of the approximate ODE's are compared with numerical solutions of the NLS equation and are found to be in very good agreement. In addition, the potential implications for obtaining improved approximate ODE models for soliton propagation in optical fibers and other devices governed by NLS-type equations, such as soliton logic gates, are discussed.

Original languageEnglish (US)
Pages (from-to)1484-1492
Number of pages9
JournalPhysical Review E
Volume51
Issue number2
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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