Solitary waves, steepening and intial collapse in the MaxwellLorentz system 
Mads Peter Sørensen, Moysey Brio, Garry Webb, Jerome V. Moloney

Abstract  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 solitontype 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. 
Keywords  Nonlinear optics; Vector Maxwell's equations; Solitary waves; Initial collapse 
Type  Journal paper [With referee] 
Journal  Physica D 
Year  2002 Vol. 170 pp. 287303 
BibTeX data  [bibtex] 
IMM Group(s)  Mathematical Physics 