Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system

Mads Peter Sørensen, Moysey Brio, Garry M. Webb, Jerome V. Moloney

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We present a numerical study of Maxwell's equations in nonlinear dispersive optical media describing propagation of pulses in one Cartesian space dimension. Dispersion and nonlinearity are accounted for by a linear Lorentz model and an instantaneous Kerr nonlinearity, respectively. The dispersion relation reveals various asymptotic regimes such as Schrödinger and KdV branches. Existence of soliton-type solutions in the Schrödinger regime and light bullets containing few optical cycles together with dark solitons are illustrated numerically. Envelope collapse regimes of the Schrödinger equation are compared to the full system and an arrest mechanism is clearly identified when the spectral width of the initial pulse broadens beyond the applicability of the asymptotic behavior. We show that beyond a certain threshold the carrier wave steepens into an infinite gradient similarly to the canonical Majda-Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities.

Original languageEnglish (US)
Pages (from-to)287-303
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Issue number3-4
StatePublished - Sep 15 2002


  • Initial collapse
  • Nonlinear optics
  • Solitary waves
  • Vector Maxwell's equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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