Related papers: Nonlinear Waves in Lattices: Past, Present, Future
This paper reviews some of our recent results in nonlinear atom optics. In addition to nonlinear wave-mixing between matter waves, we also discuss the dynamical interplay between optical and matter waves. This new paradigm, which is now…
We give a brief overview of the way atomic physics is now developing in a way reminiscent of the optics revolution of the 1960's. Thanks in particular to recent developments in atomic trapping and cooling, the new field of atom optics is…
Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic…
We review the recent developments in the field of photonic lattices emphasizing their unique properties for controlling linear and nonlinear propagation of light. We draw some important links between optical lattices and photonic crystals…
We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
We present a new concept for the generation of optical lattice waves. For all four families of nondiffracting beams, we are able to realize corresponding nondiffracting intensity patterns in one single setup. The potential of our approach…
In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…
The growing need for a better understanding of nonlinear processes in plasma physics has in the last decades stimulated the development of new and more advanced data analysis techniques. This review lists some of the basic properties one…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the…
We present a progress overview focused on the recent theoretical and experimental advances in the area of soliton manipulation in optical lattices. Optical lattices offer the possibility to engineer and to control the diffraction of light…
We consider several effects of the matter wave dynamics which can be observed in Bose-Einstein condensates embedded into optical lattices. For low-density condensates we derive approximate evolution equations, the form of which depends on…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
Recently, a lot of effort has been dedicated to developing next-generation optoelectronic devices based on two-dimensional materials, thanks to their unique optical properties that are significantly different from those of their bulk…
Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…
We study the nonlinear dynamics of wave packets in honeycomb lattices, and show that, in quasi-1D configurations, the waves propagating in the lattice can be separated into left-moving and right-moving waves, and any wave packet composed of…
We show a novel kind of nonlinear waves in two-dimensional photonic lattices. This waves take the form of light clusters that may fill an arbitrary number of lattice sites. We have demonstrated by numerical simulations that stable…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…