Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials

We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. Two short-pulse equations (SPEs) are derived for the high- and low-frequency “band gaps” (where linear electromagnetic waves are evanescent) with linear effective permittivity ϵ<0 and permeability μ>0. The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schrödinger equation are made.