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Comparisons between sine-Gordon and perturbed nonlinear Schrdinger equations for modeling light bullets beyond critical collapse

Weizhu Bao Xuanchun Dong Jack Xin

Analysis of PDEs mathscidoc:1912.43874

Physica D: Nonlinear Phenomena, 239, (13), 1120-1134, 2010.7
The sine-Gordon (SG) equation and perturbed nonlinear Schrdinger (NLS) equations are studied numerically for modeling the propagation of two space dimensional (2D) localized pulses (the so-called <i>light bullets</i>) in nonlinear dispersive optical media. We begin with the (2+1) SG equation obtained as an asymptotic reduction in the two level dissipationless MaxwellBloch system, followed by the review on the perturbed NLS equation in 2D for SG pulse envelopes, which is globally well posed and has all the relevant higher order terms to regularize the collapse of standard critical (cubic focusing) NLS. The perturbed NLS is approximated by truncating the nonlinearity into finite higher order terms undergoing focusingdefocusing cycles. Efficient semi-implicit sine pseudospectral discretizations for SG and perturbed NLS are proposed with rigorous error estimates. Numerical comparison results between light bullet
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@inproceedings{weizhu2010comparisons,
  title={Comparisons between sine-Gordon and perturbed nonlinear Schrdinger equations for modeling light bullets beyond critical collapse},
  author={Weizhu Bao, Xuanchun Dong, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210348960796438},
  booktitle={Physica D: Nonlinear Phenomena},
  volume={239},
  number={13},
  pages={1120-1134},
  year={2010},
}
Weizhu Bao, Xuanchun Dong, and Jack Xin. Comparisons between sine-Gordon and perturbed nonlinear Schrdinger equations for modeling light bullets beyond critical collapse. 2010. Vol. 239. In Physica D: Nonlinear Phenomena. pp.1120-1134. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210348960796438.
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