We describe an optical transmission line that consists of an array of wavelength-scale optical disk resonators coupled to an optical waveguide. Such a structure leads to exotic optical characteristics, including ultraslow group velocities of propagation, enhanced optical nonlinearities, and large dispersion with a controllable magnitude and sign. This device supports soliton propagation, which ...

We prove the existence and uniqueness of smooth solutions with large initial data for a system equations modeling interaction short waves, governed by nonlinear Schrodinger equation, an...

We consider two types of strongly localized modes in discrete nonlinear lattices. Taking the lattice nonlinear Schrodinger (NLS) equation as a particular but rather fundamental example, we show that (1) the discreteness effects may be understood in the "standard" discrete NLS model as arising from an effective periodic potential similar to the Peierls-Nabarro (PN) barrier potential for kinks in...

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the dr...

We derive the long-time asymptotics for solution of initial-boundary value problem coupled nonlinear Schrodinger equation whose Lax pair involves 3 × matrix in present paper. Based on a no...

We prove the scattering for a defocusing nonlinear Schrodinger equation with sum of two repulsive potentials strictly convex level surfaces, thus providing result in trapped setting similar to exterior obstacles.