相关论文: Gap Solitons and Bloch Waves in Nonlinear Periodic…

Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of…

We study the gap solitons and nonlinear Bloch waves of interacting bosons in one-dimensional optical lattices, taking into account the interaction from the weak to the strong limits. It is shown that composition relation between the gap…

We study the stability of gap solitons of the super-Tonks-Girardeau bosonic gas in one-dimensional periodic potential. The linear stability analysis indicates that increasing the amplitude of periodic potential or decreasing the nonlinear…

Phase frustration in periodic lattices is responsible for the formation of dispersionless flat bands. The absence of any kinetic energy scale makes flat band physics critically sensitive to perturbations and interactions. We report here on…

Bloch wavefunctions are used to derive dispersion relations for water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one dimensional periodicity (stripes), band gaps for wavevectors in…

We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form…

We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an…

The paper studies asymptotics of moving gap solitons in nonlinear periodic structures of finite contrast ("deep grating") within the one dimensional periodic nonlinear Schr\"odinger equation (PNLS). Periodic structures described by a finite…

We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrodinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays,…

It is shown that the periodic DNLS, with cubic nonlinearity, possesses gap solutions, i. e. standing waves, with the frequency in a spectral gap, that are exponentially localized in spatial variable. The proof is based on the linking…

The work is devoted to numerical investigation of stability of stationary localized modes ("gap solitons") for the one-dimentional nonlinear Schr\"odinger equation (NLSE) with periodic potential and repulsive nonlinearity. Two classes of…

Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BECs) loaded into optical lattices, are often described by the nonlinear Schr\"odinger/Gross-Pitaevskii equation with a sinusoidal potential. Here, we…

We show how the chiral properties of Bose Einstein condensates subject to current-density interactions and loaded in optical lattices can be observed in the realization of nonlinear Bloch states, whose spectrum lacks the usual periodic…

The formation of nonlinear Bloch states in open driven-dissipative system of exciton-polaritons loaded into a weak-contrast 1D periodic lattice is studied numerically and analytically. The condensate is described within the framework of…

We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase shift between them, in a medium with the uniform Kerr…

We study fundamental and compound gap solitons (GSs) of matter waves in one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D) weak-radial-confinement regime, which corresponds to realistic experimental conditions in…

We analyze the existence, stability, and mobility of gap solitons in a periodic photonic structure with nonlocal nonlinearity. Within the Bragg region of band gaps, gap solitons exhibit better stability and higher mobility due to the…

In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries.…

The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals. Considering…

Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically…