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

Publication: Research - peer-reviewJournal article – Annual report year: 2002

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Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system. / Sørensen, Mads Peter; Brio, Moysey; Webb, Garry; Moloney, Jerome V.

In: Physica D: Nonlinear Phenomena, Vol. 170, No. 3-4, 2002, p. 287-303.

Publication: Research - peer-reviewJournal article – Annual report year: 2002

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Author

Sørensen, Mads Peter; Brio, Moysey; Webb, Garry; Moloney, Jerome V. / Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system.

In: Physica D: Nonlinear Phenomena, Vol. 170, No. 3-4, 2002, p. 287-303.

Publication: Research - peer-reviewJournal article – Annual report year: 2002

Bibtex

@article{859338e06d4e462f9e0800bdf91fcc1d,
title = "Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system",
keywords = "Nonlinear optics; Vector Maxwell's equations; Solitary waves; Initial collapse",
publisher = "Elsevier BV North-Holland",
author = "Sørensen, {Mads Peter} and Moysey Brio and Garry Webb and Moloney, {Jerome V.}",
year = "2002",
doi = "10.1016/S0167-2789(02)00538-9",
volume = "170",
number = "3-4",
pages = "287--303",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",

}

RIS

TY - JOUR

T1 - Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system

A1 - Sørensen,Mads Peter

A1 - Brio,Moysey

A1 - Webb,Garry

A1 - Moloney,Jerome V.

AU - Sørensen,Mads Peter

AU - Brio,Moysey

AU - Webb,Garry

AU - Moloney,Jerome V.

PB - Elsevier BV North-Holland

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - Nonlinear optics; Vector Maxwell's equations; Solitary waves; Initial collapse

UR - http://www.imm.dtu.dk/pubdb/p.php?2997

U2 - 10.1016/S0167-2789(02)00538-9

DO - 10.1016/S0167-2789(02)00538-9

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3-4

VL - 170

SP - 287

EP - 303

ER -