Optical solitons in PT periodic potentials

We investigate the effect of nonlinearity on beam dynamics in parity-time (PT) symmetric potentials. We show that a novel class of one- and two-dimensional nonlinear self-trapped modes can exist in optical PT synthetic lattices. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow within these complex solitons is also examined.     

Linear superpositions of gap solitons in periodic Kerr media

The existence of a type of soliton in periodic Kerr media constructed as a superposition of noninteracting gap solitons of different kinds (bright, dark, and periodic) is first demonstrated. The periodic modulation of the nonlinearity is used to suppress the cross-phase modulation between component solitons to allow the superimposed beam to propagate for long distances.     

Vortex solitons in the semi-infinite gap of optically induced periodic lattices

Vortex solitons with a ring vortex core residing in a single lattice site in the semi-infinite gap of square optical lattices are reported. These solitons are no longer bound states of the Bloch-wave unit (Bloch-wave distribution in one lattice site) at the band edge of the periodic lattice, and consequently they do not bifurcate from the corresponding band edge. For saturable nonlinearity, one family of such solitons is found, and its existing curve forms a closed loop, which is very surprising. For Kerr nonlinearity, two families of such vortex solitons are found.     

Modulational instability and gap solitons in periodic ferromagnetic films

The modulational instability and gap solitons are theoretically studied in the ferromagnetic films under a periodic magnetic field. By multiple scale expansion, the envelope soliton solutions are obtained naturally. Due to the periodic modulation of dispersion, the solitons may be pushed into the gap region. For the easy-axis magnetic film, the red-shift of frequency leads to a modulational instability in the bottom of band and generates a bright gap soliton. For the easy-plane case, the blue-shift leads to an instability in the top of band and a dark gap soliton emerges. The weak damping produces an attenuation factor and a small oscillation.     

Taming chaotic solitons in Frenkel-Kontorova chains by weak periodic excitations

We have proposed theoretically and confirmed numerically the possibility of controlling chaotic solitons in damped, driven Frenkel-Kontorova chains subjected to additive bounded noise by weak periodic excitations. Theoretically, we obtained an effective equation of motion governing the dynamics of the soliton center of mass for which we deduced Melnikov's method-based predictions concerning the regions in the control parameter space where homoclinic bifurcations are frustrated. Numerically, we found that such theoretical predictions can be reliably applied to the original Frenkel-Kontorova chains, even for the case of localized application of the soliton-taming excitations, and there is strikingly good agreement between analytical estimates and numerical results.     

The （l＋l）-dimensional spatial solitons in media with weak nonlinear nonlocality

We study the propagation of (1+1)-dimensional spatial soliton in a nonlocal Kerr-type medium with weak nonlocality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a nonlinear Schr?dinger equation with perturbation terms. Then, an approximate analytical solution of the equation is found by the perturbation method. We also find some interesting properties of the intensity profiles of the soliton.     

Suppression of diffusion by a weak external field in periodic potentials

Diffusion of overdamped Brownian particles in sawtooth potentials subject to a spatially uniform tilt is studied focusing on the influence of a small bias. It is shown that in the potentials with an asymmetry in the direction of tilting force, the application of a weak external force leads to a suppression of diffusive motion: the diffusion coefficient as a function of bias passes through a minimum which precedes an increase of diffusion caused by delocalization of particles. In the weak noise limit the effect can be understood as a competition between the forward and backward escape rates over potential barriers determining the behaviour of the diffusion coefficient in a weak external field. The asymptotic lower border for the reduction of spreading of particles at fixed temperature is established. The decrease of diffusion is accompanied by more rapid increase of current.     

On relativistic energy band corrections in the presence of periodic potentials

A previously developed formalism to compute relativistic corrections of bound state energies for spin-1/2 particles is applied to relativistic corrections of energy bands of one-dimensional, periodic Hamiltonians. We explicitly describe Floquet theory for periodic Dirac operators on the line. Extensions including impurity potentials and/or v2 dimensions are straightforward and sketched at the end.     

Route to nonlocality and observation of accessible solitons

We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of accessible solitons and establishes an important link with parametric solitons.     

Multidimensional semi-gap solitons in a periodic potential

The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr?dinger equation with the self-defocusing cubic nonlinearity are studied. The equation describes propagation of light in a medium with normal group-velocity dispersion (GVD). Strictly speaking, solitons cannot exist in the model, as its spectrum does not support a true bandgap. Nevertheless, the variational approximation (VA) and numerical computations reveal stable solutions that seem as completely localized ones, an explanation to which is given. The solutions are of the gap-soliton type in the transverse direction(s), in which the periodic potential acts in combination with the diffraction and self-defocusing nonlinearity. Simultaneously, in the longitudinal (temporal) direction these are ordinary solitons, supported by the balance of the normal GVD and defocusing nonlinearity. Stability of the solitons is predicted by the VA, and corroborated by direct simulations.     

非局域程度对向列相液晶中空间光孤子的影响

理论分析了非局域程度对向列相液晶中(1+2)维空间光孤子的影响.得到了非线性系数以及特征长度和预倾角的关系,并且给出了强非局域性的非线性薛定谔方程,最终得到了单孤子和临界功率的解析解.实验上,通过改变偏压从而间接测量了向列相液晶中的临界功率,并与数值模拟结果相结合与理论结果进行了比较,发现基本相符. 关键词： 空间光孤子 非线性系数 非局域程度 临界功率     

Localization of solitons: linear response of the mean-field ground state to weak external potentials

Two aspects of bright matter?Cwave solitons in weak external potentials are discussed. First, we briefly review recent results on the Anderson localization of an entire soliton in disordered potentials, as a paradigmatic showcase of genuine quantum dynamics beyond simple perturbation theory. Second, we calculate the linear response of the mean-field soliton shape to a weak, but otherwise arbitrary, external potential, with a detailed application to lattice potentials.     

Discrete gap solitons in a diffraction-managed waveguide array

A model including two nonlinear chains with linear and nonlinear couplings between them, and opposite signs of the discrete diffraction inside the chains, is introduced. In the case of the cubic [ χ⁽³⁾] nonlinearity, the model finds two different interpretations in terms of optical waveguide arrays, based on the diffraction-management concept. A continuum limit of the model is tantamount to a dual-core nonlinear optical fiber with opposite signs of dispersions in the two cores. Simultaneously, the system is equivalent to a formal discretization of the standard model of nonlinear optical fibers equipped with the Bragg grating. A straightforward discrete second-harmonic-generation [ χ⁽²⁾] model, with opposite signs of the diffraction at the fundamental and second harmonics, is introduced too. Starting from the anti-continuum (AC) limit, soliton solutions in the χ⁽³⁾ model are found, both above the phonon band and inside the gap. Solitons above the gap may be stable as long as they exist, but in the transition to the continuum limit they inevitably disappear. On the contrary, solitons inside the gap persist all the way up to the continuum limit. In the zero-mismatch case, they lose their stability long before reaching the continuum limit, but finite mismatch can have a stabilizing effect on them. A special procedure is developed to find discrete counterparts of the Bragg-grating gap solitons. It is concluded that they exist at all the values of the coupling constant, but are stable only in the AC and continuum limits. Solitons are also found in the χ⁽²⁾ model. They start as stable solutions, but then lose their stability. Direct numerical simulations in the cases of instability reveal a variety of scenarios, including spontaneous transformation of the solitons into breather-like states, destruction of one of the components (in favor of the other), and symmetry-breaking effects. Quasi-periodic, as well as more complex, time dependences of the soliton amplitudes are also observed as a result of the instability development. Received 14 September 2002 / Received in final form 4 February 2003 Published online 24 April 2003 RID="a" ID="a"e-mail: malomed@eng.tau.ac.il     

Generation of upper-hybrid solitons in a weak magnetic field

A simple model is presented which describes the space—time evolution of upper-hybrid (UH) waves excited in the mode-conversion conversion process. The model predicts oscillatory UH waves due to the ion inertia effect in the weakly nonlinear regime, and an UH soliton in the strongly nonlinear regime.     

Sine-Gordon solitons in the presence of a noisy potential

We study the interaction of sine-Gordon solitons with two kinds of impurity potentials localized in space and varying randomly in time. the production of modified kink-antikink pairs is observed with different features depending respectively on the additive or multiplicative nature of the noise.     

不同非局域程度条件下空间光孤子的传输特性

光束在非局域非线性介质中传输由非局域非线性薛定谔方程描述.讨论了在不同非局域程度 条件下，空间光孤子的传输特性.提出了一个基于分步傅里叶算法数值求解孤子波形和分布 的迭代算法.假定介质的非线性响应函数为高斯型，得出了在不同非局域程度条件下空间光 孤子的数值解，并数值证明了它们的稳定性.结果表明，不论非局域程度如何，光束都能以 光孤子态在介质中稳定传输.光孤子的波形是从强非局域时的高斯型过渡到局域时的双曲正 割型，形成孤子的临界功率随非局域程度的减弱而减小，光孤子相位随距离线性增大，相位 的变化率随非局域程度的减弱而减小. 关键词： 非局域非线性薛定谔方程 空间光孤子 临界功率 相位     

Formation of gap solitons in a finite magnonic crystal

The specific features of transmission of microwave pulses through the bandgap of a magnonic crystal when three-magnon decay processes of magnetostatic waves are allowed have been experimentally investigated. It is shown that soliton-like pulses can be formed under these conditions. The experimental data are compared with the results of numerical simulation.     

Nonautonomous solitons in external potentials

Novel soliton solutions for the nonautonomous nonlinear Schr?dinger equation models with linear and harmonic oscillator potentials substantially extend the concept of classical solitons and generalize it to the plethora of nonautonomous solitons that interact elastically and generally move with varying amplitudes, speeds, and spectra adapted both to the external potentials and to the dispersion and nonlinearity variations. The nonautonomous soliton concept can be applied to different physical systems, from hydrodynamics and plasma physics to nonlinear optics and matter waves, and offer many opportunities for further scientific studies.