Exact soliton solution of spin chain with an external magnetic field in linear wave background

Employing a simple, straightforward Darboux transformation we construct exact N-soliton solution for anisotropic spin chain driven by an external magnetic field in linear wave background. As a special case the explicit one- and two-soliton solution dressed by the linear wave corresponding to magnon in quantum theory is obtained analytically and its property is discussed in detail. The dispersion law, effective soliton mass, and the energy of each soliton are investigated as well. Our result show that the stability criterion of soliton is related with anisotropic parameter and the amplitude of the linear wave.     

Soliton Transmission Research on using Dispersion Step Fiber Chain Instead of Soliton Fiber

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Perturbed soliton-like molecular excitations in a deformed DNA chain

We study the nonlinear dynamics of a deformed Deoxyribonucleic acid (DNA) molecular chain which is governed by a perturbed sine-Gordon equation coupled with a linear wave equation representing the lattice deformation. The DNA chain considered here is assumed to be deformed periodically which is the energetically favourable configuration, and the periodic deformation is due to the repulsive force between base pairs, stress in the helical backbones and due to the elastic strain force in both the strands. A multiple scale soliton perturbation analysis is carried out to solve the perturbed sine-Gordon equation and the resultant perturbed kink and antikink solitons represent open state configuration with small fluctuation. The perturbation due to periodic deformation of the lattice changes the velocity of the soliton. However, the width of the soliton remains unchanged.     

Topological solitons in Frenkel—Kontorova chains

The properties of topological defects representing local regions of contraction and extension in the Frenkel—Kontorova chains are described. These defects exhibit the properties of quasi-particles—solitons that possess certain effective masses and are capable of moving in the Peierls—Navarro potential field having the same period as that of the substrate on which the chain is situated. The energy characteristics related to soliton motion in the chain are discussed. The dynamics of highly excited solitons that can appear either during topological defect formation or as a result of thermal fluctuation is considered. The decay of such an excitation resulting in soliton thermalization under the action of a fluctuating field generated by atomic vibrations in the chain and substrate is described in terms of the generalized Langevin equation. It is shown that soliton motion can be described using a statistically averaged equation until the moment when the soliton attains the state of thermodynamic equilibrium or is captured in one of the Peierls—Navarro potential wells, after which the motion of soliton in the chain acquires a hopping (activation) character. Analytical expression describing the curve of soliton excitation decay is obtained.     

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.     

Stochastic motion of Sine-Gordon-solitons and the spin-correlation function of CsNiF3

The interaction of solitons and magnons (linear modes) of the Sine-Gordon equation is studied. The phase shift of the magnon in presence of a soliton gives rise to a shift of the position of the soliton, if magnon wave packets are considered. This leads to a stochastic part of the soliton motion in a gas of thermally activated magnons yielding an effective velocity and a diffusion constant. The influence of this effect on the solitonic part of the correlation function is discussed and compared with the recent experiment by Steiner and Kjems.     

浅海内波环境下声场时间相关特性*

浅海内波是导致声场时间相关半径减小的一个重要原因,利用2015年南海声传播起伏实验,对比分析了线性内波以及孤立子内波环境下声场时间相关半径的统计特性。实验数据表明大振幅孤立子内波的存在极大的降低了声场的时间相关半径,声场时间相关半径从线性内波环境下的1小时-3小时,降低为孤立子内波环境下的小于20分钟。利用RAM程序仿真模拟了内波环境下的声场时间相关半径,理论预报结果与实验结果相符。     

Solitons in a deformed ferromagnet with anisotropy of the easy plane type

Soliton dynamics is studied in a compressed ferromagnetic chain having anisotropy of the “easy plane” type. It is shown that there exists a soliton wave of lattice deformation which follows the magnetic soliton. Two models are considered for the connection between deformation and spins. The soliton renormalization constant is found. The effect of lattice anharmonicity is studied.     

Dynamics of twist point defects with stretching in a polymer crystal

A molecular-dynamics simulation of the behavior of a twist point defect with stretching in a chain of an equilibrium polymer crystal (“united” atoms approximation for polyethylene) is performed for immobile and mobile neighboring chains. It is shown that such a defect in a cold polymer crystal possesses soliton-type mobility. The upper limit of the spectrum of soliton velocities is found, and it is the same for both cases. The maximum possible velocity of defects is three times lower than the theoretical limit of the spectrum (which is equal to the velocity of “ torsional” sound in an isolated chain). An explanation of the reason for this discrepancy is proposed: because of the interaction of two “degrees of freedom” of the defect (twisting and stretching) the energy of a nonlinear wave is dissipated in the linear modes of the system, which results in effective friction whose magnitude depends strongly on the velocity of the defect. The “boundary of the spectrum of soliton velocities” determines the transition between regimes of strong and weak braking of defects.     

Dynamics of wave packets and soliton interaction in terms of the third-order nonlinear Schrödinger equation

We present the results of numerical study of the evolution of wave packets and envelope soliton interaction in terms of the third-order nonlinear Schrödinger equation. It is shown that an arbitrary initial pulse evolves to a few solitons and a linear quasiperiodic wave. The interaction of solitons is accompanied by the radiation of part of the wave field in the form of a linear quasiperiodic wave from the interaction region, amplification of the soliton with larger amplitude and attenuation of the soliton with smaller amplitude.     

On the path length of an excess electron interacted with optical phonons in a molecular chain

We show that in a molecular chain with dispersionless phonons at zero temperature, a “quasistationary” moving soliton state of an excess electron is possible. As the soliton velocity vanishes, the path length of the excess electron exponentially tends to infinity. It is demonstrated that in the presence of dispersion, when the soliton initial velocity exceeds the maximum group velocity of the chain, the soliton slows down until it reaches the maximum group velocity and then moves stationarily at this maximum group velocity. A conclusion is made of the fallacy of some works were the existence of moving polarons in a dispersionless medium is considered infeasible.     

Influence of Spectral Filtering and Nonlinear Gain on an Optical Soliton

Using the direct soliton perturbation theory, we investigate the evolution of soliton parameters and the firstorder correction of bright soliton in a system with linear and nonlinear gain （or loss） and spectral filtering in a comprehensive way. The results obtained by means of our analytic method are consistent with numerical simulations. It is also found that the stable soliton propagation which has been investigated in a previous report by others is the limit case of our results.     

Inhomogeneous states and the mechanism of magnetization reversal of a chain of classical dipoles

The inhomogeneous states (solitons) in a single chain of classical dipoles are studied numerically and analytically. An analytical solution to the problem is based on the long-wave approximation for dipole sums which holds for high magnetic fields perpendicular to the dipole chain. The analytical and numerical solutions are in reasonable agreement. The magnetization reversal is investigated by numerical simulation based on the Landau-Lifshitz stochastic equations. It is demonstrated that the magnetization reversal of a dipole chain at a finite temperature has a thermal activation nature and occurs through the formation of a stable phase nucleus (a soliton at the edge of the chain) and its growth (the motion of the soliton along the chain).     

Special Property of Group Velocity for Temporal Dark Soliton

We investigate the speed of temporal dark soliton based on an optical coherent medium. It is demonstrated that the temporal dark soliton is described by a nonlinear Schrodinger equation whose coefficients are decided by the coherent medium. It is found that the speed of temporal dark soliton not only relies on the linear responses including GV parameter, group velocity dispersion parameter as well as the amplitude of dark soliton, but also relies on the nonlinear response like self-phase modulation parameter. Additionally, the dark soliton in anomalous-dispersion regime propagates slower than bright soliton, while in normal-dispersion regime it inversely propagates faster than bright soliton. The complicated property of the speed for dark soliton is quite different from the bright soliton whose speed is commonly only related to the group velocity parameter. We attribute this feature to the modulation instability of the nonlinear system.     

ON THE BREAKDOWN OF A LONG STREAK IN A TRANSITIONAL BOUNDARY LAYER

Transition in regular K-regime of boundary layer is studied. The features of the long streak that is considered as a form of soliton/like coherent structure (CS-soliton) are investigated briefly. The experiment shows that the breakdown of long streak is generated by chain of ring-like vortices.     

A Novel Envelope Soliton Solution to the Granular Crystal Model

A theoretical work on envelope solitons to a one-dimensional granular chain model is reported. In the small amplitude approximation, we analytically solve the equation of motion with the help of the semidiscrete multiple-scale method. Our results show that the granular chain model can support an asymmetric high-order envelope soliton under the certain condition. It is found that the second-harmonic term of this high-order envelope soliton has an additional phase. In addition, the influence of both the material parameter and the static load on the localized features of the high-order envelope soliton is discussed.     

Bloch oscillations of a soliton in a molecular chain

This paper presents the results of numerical experiments simulating Bloch oscillations of solitons in a deformable molecular chain subject to a constant electric field. By using as an example a homogeneous polynucleotide chain, it is shown that the system under consideration can exhibit complicated dynamical behaviour: when subject to field intensities less than a certain critical value, a soliton exhibits oscillations as a whole, while at field intensities exceeding this threshold, the soliton becomes a breather that oscillates. It is shown that the motion of a charge in a deformable chain is infinite, which in contrast to that in a rigid chain.     

Chain length dependence of localized vibrational modes around a soliton in trans-polyacetylene

Vibrational frequencies of finite polyacetylene with a charged soliton are calculated using the molecular orbital method. It is found that the frequency of the translational mode has a remarkable length effect and is inversely proportional to the square of chain length. The dependence is explained by regarding the soliton as a quantum particle in a one dimensional box.     

利用光孤子机制实现超宽范围波长调谐的理论和实验研究

以获得光参量啁啾脉冲放大系统主激光与抽运光两种波长、宽带、超短脉冲的产生及精密同步为目标,探索采用光孤子机制实现超宽带宽范围的可调谐超短脉冲产生. 数值模拟了孤子传输过程中的时域-频域演化过程及与其他非线性效应的相互作用过程和特性. 实验验证了利用光孤子机制产生可调谐脉冲的方法. 同时还观察到孤子的形成、分裂、自频移等现象,在可见光到近红外波段都演示了波长可调谐的输出特性,并且与理论分析结果符合较好. 关键词： 光参量啁啾脉冲放大 可调谐脉冲产生 非线性薛定谔方程 孤子机制     

Comparison of soliton robustness with respect to polarization-mode dispersion with first-order polarization-mode dispersion compensated linear systems

Soliton robustness to polarization-mode dispersion (PMD) is compared, both analytically and numerically, with that of linear pulses that use first-order PMD compensation. It is found that soliton robustness to PMD is comparable with first-order PMD compensation and in some cases is even better. The effects of soliton control methods on soliton robustness to PMD were also investigated, and it was found that soliton control methods can significantly improve the soliton's robustness to PMD, particularly for long-distance systems.