Nonlinear Localized Waves in a Periodic Medium

Nonlinear localized waves in a periodic medium.

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.

Nonlinear guided waves and spatial solitons in a periodic layered medium

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...

Localized waves in nonlinear oscillator chains.

This paper reviews results about the existence of spatially localized waves in nonlinear chains of coupled oscillators, and provides new results for the Fermi-Pasta-Ulam (FPU) lattice. Localized solutions include solitary waves of permanent form and traveling breathers which appear time periodic in a system of reference moving at constant velocity. For FPU lattices we analyze the case when the ...

On Nonlinear Water Waves in a Channel

Nonlinear Waves on Localized and Periodic Backgrounds with Time-Space Modulation

We present one family of general analytical solutions for the generalized nonlinear Schrödinger equation with time-space modulation via the method of a combination of the Darboux transformation and similarity transformation. Nonlinear waves on different localized and periodic backgrounds depending on the corresponding nonlinearity modulations are obtained. In particular, we demonstrate the exis...