相关论文: Exponentially localised interface eigenmodes in fi…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…
We present the discovery of a novel and intriguing global geometric structure of the (interior) transmission eigenfunctions associated with the Helmholtz system. It is shown in generic scenarios that there always exists a sequence of…
The aim of this article is to advance the field of metamaterials by proposing formulas for the design of high-contrast metamaterials with prescribed subwavelength defect mode eigenfrequencies. This is achieved in two settings: (i) design of…
We show that defect modes in infinite systems of resonators have corresponding modes in finite systems which converge as the size of the system increases. We study the generalized capacitance matrix as a model for three-dimensional coupled…
In the present work, we generalize earlier considerations for intrinsic localized modes consisting of a few excited sites, as developed in the one-component discrete nonlinear Schrodinger equation model, to the case of two-component…
Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems such as two-frequency forced Faraday waves, we study the interaction of two spatially periodic modes that are nearly resonant. Within the…
This work extends the theory of topological protection to dispersive systems. This theory has emerged from the field of topological insulators and has been established for continuum models in both classical and quantum settings. It predicts…
The aim of this paper is to illustrate both analytically and numerically the interplay of two fundamentally distinct non-Hermitian mechanisms in a deep subwavelength regime. Considering a parity-time symmetric system of one-dimensional…
We consider the localized modes (bright solitons) described by one-dimensional quintic nonlinear Schrodinger equation with a periodic potential. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show…
We show that resonant frequencies of a system of coupled resonators in a truncated periodic lattice converge to the essential spectrum of corresponding infinite lattice. We use the capacitance matrix as a model for fully coupled resonators…
Bound states at interfaces between superconductors and other materials are a powerful tool to characterize the nature of the involved systems, and to engineer elusive quantum excitations. In-gap excitations of conventional s-wave…
We study finite quantum wires and rings in the presence of a charge density wave gap induced by a periodic modulation of the chemical potential. We show that the Tamm-Shockley bound states emerging at the ends of the wire are stable against…
We investigate internal localized eigenmodes of the linearized equation around spin discrete breathers in 1D antiferromagnets with on-site easy axis anisotropy. The threshold of occurrence of the internal localized eigenmodes has a typical…
We introduce a discrete linear lossy system with an embedded "hot spot" (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective…
We report experiments on spatial switching dynamics and steady state structures of passive nonlinear semiconductor resonators of large Fresnel number. Extended patterns and switching front dynamics are observed and investigated. Evidence of…
We analyze a (1+1)-dimension directed random walk model of a polymer dipped in a medium constituted by two immiscible solvents separated by a flat interface. The polymer chain is heterogeneous in the sense that a single monomer may…
This paper shows that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate…
The question of whether the topological insulators can host a stable nontrivial phase in the presence of spatially correlated disorder is a fundamental question of interest. Based on theoretical investigations, we analyze the effect of…
We consider the eigenvalue problem for one-dimensional linear Schr\"odinger lattices (tight-binding) with an embedded few-sites linear or nonlinear, Hamiltonian or non-conservative defect (an oligomer). Such a problem arises when…
Mathematical modeling of resonant waves propagating in 2D periodic infinite lattices is conducted. Rectangular-cell, triangular-cell and hexagonal-cell lattices are considered. Eigenvalues (here eigenfrequencies) of steady-state problems…