The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized...

We report a mechanism to obtain optical pulling or pushing forces exerted on the active dispersive chiral media. Electromagnetic wave equations for the pure chiral media using constitutive relations containing dispersive Drude models are numerically solved by means of Auxiliary Differential Equation Finite Difference Time Domain (ADE-FDTD) method. This method allows us to access the time averag...

A high-order discontinuous Galerkin time-domain (DGTD) method for Maxwell’s equations for dispersive media of Drude type is derived and then used to study the coupling of 2D silver nanowires, which have potential applications in optical circuits without the restriction of diffraction limits of traditional dielectric waveguides. We have demonstrated the high accuracy of the DGTD for the electrom...

We present discrete energy decay results for the Yee scheme applied to Maxwell’s equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme in a nondispersive dielectric. However, energy decay for the Maxwell-Debye and Ma...

We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and initial data contain inverse of small parameter , typical solutions oscillate frequency proportional to in time space. Moreover, have be computed on intervals length order study nonlinear diffractive effects. As consequence, direct numerical simulations are extremely costly or even imposs...