Modeling light bullets with the two-dimensional sineGordon equation

Jack Xin

Analysis of PDEs mathscidoc:1912.43844

Physica D: Nonlinear Phenomena, 135, 345-368, 2000.1
Light bullets are spatially localized ultra-short optical pulses in more than one space dimensions. They contain only a few electromagnetic oscillations under their envelopes and propagate long distances without essentially changing shapes. Light bullets of femtosecond durations have been observed in recent numerical simulation of the full Maxwell systems. The sineGordon (SG) equation comes as an asymptotic reduction of the two level dissipationless MaxwellBloch system. We derive a new and complete nonlinear Schrdinger (NLS) equation in two space dimensions for the SG pulse envelopes so that it is globally well-posed and has all the relevant higher order terms to regularize the collapse of the standard critical NLS (CNLS). We perform a modulation analysis and found that SG pulse envelopes undergo focusingdefocusing cycles. Numerical results are in qualitative agreement with asymptotics and
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@inproceedings{jack2000modeling,
  title={Modeling light bullets with the two-dimensional sineGordon equation},
  author={Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210141110683408},
  booktitle={Physica D: Nonlinear Phenomena},
  volume={135},
  pages={345-368},
  year={2000},
}
Jack Xin. Modeling light bullets with the two-dimensional sineGordon equation. 2000. Vol. 135. In Physica D: Nonlinear Phenomena. pp.345-368. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210141110683408.
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