Almost periodic behavior of nonlinear waves

Almost Periodic Oscillations and Waves

Waves in almost periodic particle chains

Almost periodic particle chains exhibit peculiar propagation properties that are not observed in perfectly periodic ones. Furthermore, since they inherently support nonnegligible long-range interactions and radiation through the surrounding free space, nearest-neighbor approximations cannot be invoked. Hence the governing operator is fundamentally different from that used in traditional analysi...

Almost Periodic Solutions of Second Order Nonlinear Differential Equations with Almost Periodic Forcing

Two-dimensional Waves Around Almost Periodic Arrangements of Scatterers∗

Acoustic waves around an infinite configuration of identical circular scatterers are considered. Each scatterer is close to a node of a regular lattice: the geometrical configuration is almost periodic. Analytical estimates for the average field in such a random medium are obtained. Introduction Consider waves in a two-dimensional periodic structure, defined by a lattice Λ: each cell in the lat...

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.