Ultrashort pulses and short-pulse equations in 2+1 dimensionsPhysical Review A (2012)
AbstractIn 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 DateAugust 23, 2012
Citation InformationY. 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)
Available at: http://works.bepress.com/panos_kevrekidis/206/