On the dynamics of excitations in disordered systems

A new, time-local (TL) reduced equation of motion for the probability distribution of excitations in a disordered system is developed. ToO(k²) the TL equation results in a Gaussian spatial probability distribution, i.e, P(r, t) = [(2)^1/2]^–dexp(-r²/2²), where = (t) is a correlation length, andr = ¦r¦. The corresponding distribution derived from the Hahn-Zwanzig (HZ) equation is more complicated and assumes the asymptotic (r ) form: P(r, s)(s ^d )^–1exp(–r/) · (r/)^(1-d)/2 where = (s),d is the space dimensionality, ands is the Laplace transform variable conjugate tot. The HZ distribution generalizes the scaling form suggested by Alexanderet al. ford= 1. In the Markov limit (t)t, (s)1/s, and the two distributions are identical (ordinary diffusion).     

Nonlinear nanoscale localization of magnetic excitations in atomic lattices

Reviewed here is the nonlinear intrinsic localization expected for large amplitude spin waves in a variety of magnetically ordered lattices. Both static and dynamic properties of intrinsic localized spin wave gap modes and resonant modes are surveyed in detail. The modulational instability of extended nonlinear spin waves is discussed as a mechanism for dynamical localization of spin waves in homogeneous magnetic lattices. The interest in this particular nonlinear dynamics area stems from the realization that some localized vibrations in perfectly periodic but nonintegrable lattices can be stabilized by lattice discreteness. However, in this rapidly growing area in nonlinear condensed matter research the experimental identification of intrinsic localized modes is yet to be demonstrated. To this end the study of spin lattice models has definite advantages over those previously presented for vibrational models both because of the importance of intrasite and intersite nonlinear interaction terms and because the dissipation of spin waves in magnetic materials is weak compared to that of lattice vibrations in crystals. Thus, both from the theoretical and the experimental points of view, nonlinear magnetic systems may provide more tractable candidates for the investigation of intrinsic localized modes which display nanoscale dimensions as well as for the future exploration of the quantum properties of such excitations.     

Nonlinear dynamics and collective excitations of spin-1 magnets

The Poisson brackets for macroscopic parameters are obtained and nonlinear dynamic equations of spin-1 magnets are derived. Two types of magnetic exchange Hamiltonians corresponding to two Kazimir invariants of SU(3) group are introduced. Thermodynamics of spin-1 magnets is studied and the flux densities of additive integrals of motion are found in terms of exchange energy density. The momentum of magnons is introduced and the corresponding dynamic equation is derived. The spectra of spin and quadrupole waves of magnets with various symmetry of equilibrium state with respect to time inversion are found.     

Boiti-Leon-Pempinelli系统的新变量分离解及其方形孤子和分形孤子

利用拓展的Riccati方程映射法，得到了(2+1)维Boiti-Leon-Pempinelli系统新的变量分离 解．根据得到的分离变量解，构造出该系统新型的孤子结构——方孤子和分形孤子． 关键词： Boiti-Leon-Pempinelli系统 拓展Riccati映射 方形孤子 分形孤子     

Nonlinear switching and solitons in PT‐symmetric photonic systems

One of the challenges of the modern photonics is to develop all‐optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity‐Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non‐conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT‐symmetric photonic systems with an intensity‐dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly‐induced PT‐symmetry breaking, and all‐optical switching. Nonlinear PT‐symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

     

Effect of friction on the dynamics and kinematics of solitons in Frenkel-Kontorova systems

To describe the motion of a soliton in ideal Frenkel-Kontorova systems at energies above the amplitude of the Peierls-Navarro pinning potential (PNP), a dynamic Langevin equation with stochastic friction force was proposed: ÿ + α? ? βsin2πy = 0, where y is the dimensionless coordinate of the soliton in units of the substrate potential period, which is determined by the first moment of the soliton shape according to the standard procedure; differentiation is performed with respect to the dimensionless time τ = t(κ/m)^1/2, where κ is the force constant of the chain bond and m is the mass of a chain element. A procedure for determining the friction coefficient α is discussed. Numerical calculations of the dependences of the coordinate and velocity of the soliton on the time over wide ranges of initial conditions and parameters α and β. An analysis of the calculation results showed that the motion of the soliton slows down exponentially, being modulated as it does by the action of the PNP, and end up at one of the minima of the PNP.     

Interaction dynamics of bright solitons in linearly coupled asymmetric systems

In this research work, composite media based on metamaterials including random distribution of spherical nanoparticles in a polymeric foam host are suggested to achieve negative effective refractive index in the visible spectrum. For this purpose structures including single, two and three layer spherical particles are investigated. Based on simulation results, media including single layer spheres (metallic and dielectric particles) and two layer nanospheres (core–shell particles consist of metallic core and dielectric shell) based on superposition of nanoparticles with different sizes and fill fractions are proposed for desired result. In this work, to obtain optimized band with negative RI media, superposition of three layer nanoparticles and doped semiconductor are designed.

     

Nonlinear excitations in the critical region

The free energy transformation due to fluctuations is investigated in an exactly solvable model. This model accounts for the fluctuation interaction in a reduced manner and leads to a realistic estimation for the free energy. In particular it gives a nice critical exponent=5. It is shown that in spite of the monotonic character of the effective free energy in the critical region the properties of the system should be described on the basis of the ⁶ model. Localized nonlinear excitations are found to be possible with a profile rather like that known as a bump near the point of the first-order phase transition.     

对称混沌系统的非线性动力学行为及控制

基于线性反馈控制思想，提出了一种对称动力学系统及其控制混沌的方法，给出了预期各周期轨道反馈系数的选择原则，适当选择反馈系数，即可得到不同的周期轨道.将此方法应用 到Logistic映射中，取得了良好的控制效果. 关键词： 反馈控制 周期转道 对称系统     

Nonlinear surface waves and solitons

First a general introduction on the notion of surface waves on solids (types of different waves), a reminder on the simplest familiar nonlinear dispersive model equations, and another on the basic equations of nonlinear elasticity are given. Then attention is focused on the linear surface wave problem. The main properties of nonlinear surface waves in the absence of dispersion are studied next by use of several asymptotic techniques. The additional effects of dispersion are then considered and combined with those of nonlinearity with an emphasis on the case of so-called shear-horizontal surface waves and solitary-wave solutions for envelope signals. Finally, typical nonlocality is introduced for nonlinear Rayleigh surface waves, and general comments on more general two-dimensional (in propagation space) nonlinear strain waves on structures are evoked by way of conclusion.     

Spectroscopy of collective excitations in interacting low-dimensional many-body systems using quench dynamics

We study the problem of rapid change of the interaction parameter (quench) in a many-body low-dimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.     

Spectral-discrete solitons and localization in frequency space

We report families of discrete optical solitons in frequency space, or spectral-discrete solitons existing in a dispersive Raman medium, where individual sidebands are coupled by coherence. The associated time-domain patterns correspond either to trains of ultrashort pulses or to weakly modulated waves. We describe the physics behind the spectral localization and study soliton bifurcations, stability, and dynamics.     

Nonlinear excitations (solitons) in the antiferromagnetic chain of (NH4)2Mn0.98Fe0.02F5

Measurements of the⁵⁷Fe Mössbauer effect and of the magnetic susceptibilities on a single crystal have been performed on the quasi-1-d antiferromagnetic chain of (NH₄)₂Mn_0.98Fe_0.02F₅ as a function of temperature. Particular attention was paid to the region very near the Néel point. The Mössbauer spectra fitted by the Blume-Tjon model show definite relaxation effects, which are attributed to short-range order with temperature-dependent relaxation times. The soliton model of nonlinear excitations was applied. Experimental data confirm the predicted exponential temperature dependence of the thermal excitation of moving domain walls. From the activation energy a local anisotropy energyD/k of –3.9 K was derived.     

Nonlinear network dynamics on earthquake fault systems

Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.     

Nonlinear compression of optical solitons

In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single field in a fiber medium with phase modulation and fibre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modified NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.     

孤子和辐射场的非线性相互作用

利用穿衣服的方法推导出了在纯辐射场情况下Jost函数对的显式,由此得到了孤子与辐射场相互作用的解析表达式,发现脉冲在传输过程中,由于受到辐射场的作用,其振幅的演化在传播方向上是按照幂指数的负的平方根的规律衰减,并且将最终演化成一个类孤子的形式,且阐明了因子γ对光脉冲输出的光谱特性将会产生重要影响;并对辐射场的存在对类孤子演化的动力学行为作了分析. 关键词： 穿衣服方法 类孤子 孤子 辐射场