A global nonlinear stability analysis is performed for a couple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is important because it shows that lineari...

A simple scheme to steer optical beams is proposed. The basic idea is to impose a sinusoidal phase modulation on the optical beam and then propagate it in a nonlinear Kerr medium. Spatial phase modulation splits the input beam into multiple subbeams, while the nonlinear medium shapes a particular subbeam into a spatial soliton in such a way that most of the beam power appears in a narrow beam w...

We analyze the existence and stability of nonlinear localized waves described by the Kronig-Penney model with a nonlinear impurity. We study the properties of such waves in a homogeneous medium, and then analyze new effects introduced by periodicity of the medium parameters. In particular, we demonstrate the existence of a novel type of stable nonlinear band-gap localized states, and also revea...

A model is introduced to describe guided propagation of a linear or nonlinear pulse which encounters a localized nonlinear defect, that may be either static or breather-like one. The model with the static defect directly applies to an optical pulse in a long fiber link with an inserted additional section of a nonlinear fiber. A local breather which gives rise to the nonlinear defect affecting t...

We present an overview of the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by linear and nonlinear waveguides. First we consider a single layer with a cubic nonlinear response (a nonlinear slab waveguide) embedded in a periodic layered linear medium and describe nonlinear localized modes (guided waves and Bragg-like localized g...