mBBM方程的双扭结孤立波及其动力学稳定性

采用双曲函数展开法得到Modified Benjamin-Bona-Mahony（mBBM）方程的一类扭结-反扭结状的双扭结孤立波解,在不同的极限情况下,此孤立波分别退化为mBBM方程的扭结状和钟状孤立波解.对双扭结型单孤子的结构特征进行分析,构造有限差分格式对其动力学稳定性进行数值研究.有限差分格式为两层隐式格式,在线性化意义下无条件稳定.数值结果表明mBBM方程的双扭结型单孤子在不同类型的扰动下均具有很强的稳定性.对双孤立波的碰撞进行数值模拟,发现既存在弹性碰撞也存在非弹性碰撞.     

Propagation and collision of compacton-like kinks in Klein—Gordon lattice system

We study the propagation and collision of the compacton-like kinks in the system of an anharmonic lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compacton-like kinks is related to the nonlinear coupling parameter Cnl and the potential barrier height V0 of the double well potential. The velocity of the propagation of the compacton-like kinks is determined by the linear coupling parameter Cl, the nonlinear coupling parameter Cnl and the localization parameter q. Numerical experiments demonstrate that appropriate Cl is not detrimental to a stable propagation of the compacton-like kinks. However, the collision of compacton-like kinks and anti-kinks in the lattice with comparatively small Cl leads to the emergence of a discrete stationary breather and small amplitude nonlinear oscillation background, while moderate Cl results in the emergence of two deformed kinks with radiating oscillations and lower propagation velocities.     

Bragg guiding of domainlike nonlinear modes and kink arrays in lower-index core structures

We introduce a novel class of stable nonlinear modes trapped in a lower-index film core sandwiched between two optical lattices, or in the cylindrical core of a radial lattice, imprinted in defocusing media. Such a family of nonlinear modes transforms into defect lattice solitons when the core width is sufficiently small or into an array of kinks when the width is large enough. We find that higher-order modes with multiple zeros inside the guiding core can be stable in one-dimensional settings.     

Discreteness effects on non-topological kink soliton dynamics in nonlinear lattices

We show that discreteness effects which are known to exist for topological solitons exist also for non-topological kink solitons in nonlinear lattices. Extending the technique previously proposed for topological kinks we exhibit three cases where the properties of narrow kinks in nonlinear lattices are qualitatively different. Supersonic solitons in a monoatomic chain can propagate at constant speed without losing energy due to discreteness. Subsonic kinks in a monoatomic chain permanently radiate small amplitude oscillations. In a diatomic chain both supersonic and subsonic kinks lose energy due to discreteness. The characteristics of the small amplitude oscillations radiated by the kinks, when they exist, are well determined by our theoretical approach. Additional weak nonlinear effects are also described and discussed.     

Massless and quantized modes of kinks in the phase space of superconducting gaps

We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory.     

Kink dynamics in the highly discrete sine-Gordon system

We study kink dynamics in a very discrete sine-Gordon system where the kink width is of the order of the lattice spacing. Numerical simulations exhibit new properties of kinks in this case: they lose the memory of their initial velocity and propagate preferentially at well-defined velocities which correspond to quasi-steady states, while a kink moving at other velocities suffers relatively high rates of radiation of small amplitude oscillations. When a small external driving force is applied to the system, the same velocities appear as plateus in the strongly nonlinear mobility of the kink. The energy radiated by the kink is calculated for a simple model that preserves the discrete character of the system, and the preferential velocities for the kink are obtained to good accuracy. Similar results may be expected to be valid for other discrete systems manifesting topological solitons. The numerical simulations reveal also new stable “multiple-kink” excitations which can propagate almost freely in extremely discrete systems where “ordinary” simple kinks are pinned to the lattice by discreteness. The stability of the “multiple-kinks” is discussed.     

A class of (1 + 1) dim models that generalize the Sine-Gordon model and some properties of their solutions

In this talk we discuss the models recently presented by Bazeia et al. We present various properties of their kink-like solutions and, in particular, the properties of these kinks when they scatter on potential obstructions. We also discuss the issue of the existence of stable breather-like and multikink configurations in these models.     

铝-0.5%铜合金中反常振幅效应内耗峰的进一步实验和位错弯结气团模型

用低频扭摆进一步研究了在Al-0.5％Cu合金中观察到反常位错内耗峯的条件。结果指出,对于完全退火的试样来说,需要有适当的冷加工量,但是对于高温淬火试样则不需要冷加工。用位错气团模型定性地解释了过去所观测到的表现反常振幅效应的时效内耗峯和温度内耗峯;同时指出,简单的气团模型在作定量的解释时,遇到了下述的困难:(i)在测量内耗所用的交变应力的作用下,位错线所能够拖着气团移动的距离太短。(ii)为了气团能够被位错拖着移动,组成气团的溶质原子必须具有比通常大很多个数量级的扩散系数。(iii)根据气团模型,从理论上计算出来的使位错拖着气团以临界速度而移动时,所需的临界应力比观测值大几百倍。提出了溶质原子沿着位错弯结而扩散的气团模型,这个改进模型能够初步解决上述困难,并能定性地解释所观测的结果。这个模型所依据的基本假设是,要观测到反常内耗现象,位错线上必须具有一定数目的弯结。要得到这种弯结,可以对于退火试样进行适量的冷加工,或者把试样从高温淬火。带着弯结的位错线能够通过弯结的沿边运动而实现垂直于位错线方向的移动。可以假定,气团只在弯结两端的直位错段处形成,在弯结本身上并不形成气团。在弯结的沿边振动的过程中,聚集在弯结两端的溶质原子可以沿着位错管道进行来回的短程扩散。已知沿着位错管道的扩散具有比在正常晶体点阵中扩散时大得多的扩散系数。     

Kink defects in linear chain molecules-structure analysis based on spot and continuous diffuse electron diffraction intensities

Calculated defect diffuse scattering patterns, using the kink defect model employed earlier to explain changes in Bragg electron diffraction intensities for heated n-paraffins, are shown to account best for observed diffuse data from solution-grown and epitaxially grown micro-crystals. The presence of significant diffuse scattering below 15°K, moreover, indicates that such chain kinks are stable in the crystal lattice.     

Dynamics of dark solitons in elongated Bose-Einstein condensates

We find two types of moving dark soliton textures in elongated condensates: nonstationary kinks and proper dark solitons. The latter have a flat notch region and we obtain the diagram of their dynamical stability. At finite temperatures the dynamically stable solitons decay due to the thermodynamic instability. We develop a theory of their dissipative dynamics and explain experimental data.     

Dynamics of kinks in modulated crystals

The dynamics of kinks (domain walls) in a linear chain system with frustration, in which incommensurate phases occur, is studied. In this both numerical and analytical techniques are used. The kinks, which can be interpreted as discommensurations in incommensurate phases, are found to be unstable, in a continuum approximation, but their lifetime may be long near the lock-in transition due to pinning effects.     

Frustrated spin model as a hard-sphere liquid

We show that one-dimensional topological objects (kinks) are natural degrees of freedom for an antiferromagnetic Ising model on a triangular lattice. Its ground states and the coexistence of spin ordering with an extensive zero-temperature entropy can easily be understood in terms of kinks forming a hard-sphere liquid. Using this picture we explain effects of quantum spin dynamics on that frustrated model, which we also study numerically.     

Walk-off and pattern selection in optical parametric oscillators

The effect of walk-off in pattern selection in optical parametric oscillators is theoretically examined. We show that a dynamic mechanism also allows us to observe the formation of structures for positive signal detunings. In this regime the pattern that is generated is a periodic array of kinks that separate regions in which one of two stable steady states is alternately selected. This structure can be regarded as a train of dark soliton stripes because the two solutions have opposite signs. The wavelength of the selected pattern is theoretically predicted, and the prediction agrees with the results of the numerical solutions of the equations governing the device.     

Anomalous kinetics of dislocation kinks in a disordered dislocation-adsorbed impurity atmosphere

It is shown that the statistical fluctuations in the distribution of dislocation-adsorbed impurities change the character of the dislocation mobility because of the transition to an anomalous regime of motion of kinks. The characteristics of the corresponding dynamic phase transition are dependent on the interaction between adsorbed impurities, which can either increase or decrease the amplitude of fluctuations in the potential for kinks, depending on the sign of the interaction. The results of the calculations can also be used to describe the kinetics of one-dimensional systems of other physical nature.     

Kinematics of the forced and overdamped sine-Gordon soliton gas

Motion of a driven and heavily damped sine-Gordon chain with a low density of kinks and tight coupling between particles is controlled by the nucleation and subsequent annihilation of pairs of kinks and antikinks. We show that in the steady state there are no spatial correlations between kinks or between kinks and antikinks. For a given number of kinks and antikinks all geometrical distributions are equally alike, as in equilibrium. A master equation for the probability distribution for the number of kinks on a finite chain is solved, and substantiates the physical reasoning in previous work. The probability distribution characterizing the spread along the direction of particle motion of a finite chain in equilibrium as well as in the driven overdamped case is derived by simple combinatorial considerations. The spatial spread of a driven chain in the thermodynamic limit does not approach a steady state; a given particle followed in time deviates as t^1/2 from its average forced motion. This result follows from the hydrodynamic equations for the dilute kink gas. Comparison is made with other recent results.     

mKdV方程的双扭结单孤子及其稳定性研究

基于双曲函数法的思想,通过选择新的展开函数,得到了modified Korteweg-de Vries(mKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为mKdV方程的扭结状或钟状孤波解.文中对双扭结型孤子解的稳定性进行了数值研究,结果表明:在长波和短波简谐波扰动、钟型孤立波扰动与随机扰动下,该孤子均稳定.     

Dynamics of kinks: nucleation, diffusion, and annihilation

We investigate the nucleation, annihilation, and dynamics of kinks in a classical (1+1)-dimensional straight phi(4) field theory at finite temperature. From large scale Langevin simulations, we establish that the nucleation rate is proportional to the square of the equilibrium density of kinks. We identify two annihilation time scales: one due to kink-antikink pair recombination after nucleation, the other from nonrecombinant annihilation. We introduce a mesoscopic model of diffusing kinks based on "paired" and "survivor" kinks and antikinks. Analytical predictions for the dynamical time scales, as well as the corresponding length scales, are in good agreement with the simulations.     

Translationally invariant kink solutions of discrete ϕ<Superscript>4</Superscript> models

The properties of translationally invariant kinks in two discrete ϕ⁴ models are compared with those of the kinks in a classical discrete model. The translationally invariant kink solutions can be found randomly with respect to the lattice sites, i.e., their Peierls–Nabarro potential is exactly equal to zero. It is shown that these solutions have a Goldstone mode, that is, they can move along the lattice at vanishingly small velocities. Thus, the translationally invariant kink is not trapped by the lattice and can be accelerated by an arbitrary small external field and, having an increased mobility, can transfer a range of physical quantities: matter, energy, momentum, etc.     

Kohn anomalies and electron-phonon interactions in graphite

We demonstrate that graphite phonon dispersions have two Kohn anomalies at the Gamma-E(2g) and K-A'1 modes. The anomalies are revealed by two sharp kinks. By an exact analytic derivation, we show that the slope of these kinks is proportional to the square of the electron-phonon coupling (EPC). Thus, we can directly measure the EPC from the experimental dispersions. The Gamma-E(2g) and K-A'1 EPCs are particularly large, while they are negligible for all the other modes at Gamma and K.     

Magnetohydrodynamic kinks in astrophysics

Three-dimensional magnetic kinks in nonresistive plasmas may be created and annihilated in pairs and conserve their homotopy properties during their lifetime. Such kinks could prove relevant to astrophysical, geophysical, or laboratory plasma problems. We describe magnetic kinks with one axis of rotational invariance analytically and graphically. As an example, we examine their relevance to the puzzle of the origin of galaxies.Supported by the est Foundation and the National Science Foundation.