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Ultrashort pulses and short-pulse equations in 2+1 dimensions
Physical Review A (2012)
  • Y. Shen
  • N. Whitaker
  • Panos Kevrekidis, UMASS, Amherst
  • N. L. Tsitsas
  • D. J. Frantzeskakis
In this paper, we derive and study two versions of the short pulse equation (SPE) in (2 + 1) dimensions. Using Maxwell’s equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab wave guides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting (2 + 1)-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort one-dimensional breathers appear to be fairly robust, while rather general two-dimensional localized initial conditions are transformed into quasi-one-dimensional dispersing wave forms.
Publication Date
August 23, 2012
Publisher Statement
DOI: 10.1103/PhysRevA.86.023841
Citation Information
Y. Shen, N. Whitaker, Panos Kevrekidis, N. L. Tsitsas, et al.. "Ultrashort pulses and short-pulse equations in 2+1 dimensions" Physical Review A Vol. 86 Iss. 2 (2012)
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