Lasing on nonlinear localized waves in curved geometry

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 ...

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.

On Nonlinear Water Waves in a Channel

Nonlinear surface waves in arrays of curved waveguides

We study both theoretically and experimentally the nonlinear surface waves at the edge of curved waveguide arrays with a surface defect. We show that the nonlinear coupling between different linear modes supported by the array can lead to beam switching to different output waveguides with increasing of the nonlinearity strength. Our experimental observations are in good agreement with the numer...

Existence of Eigenvalues of a Linear Operator Pencil in a Curved Waveguide - Localized Shelf Waves on a Curved Coast

The study of the possibility of existence of the non-propagating, trapped continental shelf waves (CSWs) along curved coasts reduces mathematically to a spectral problem for a selfadjoint operator pencil in a curved strip. Using the methods developed in the setting of the waveguide trapped mode problem, we show that such CSWs exist for a wide class of coast curvature and depth profiles.