具有周期非均匀扰动的色散管理系统中的孤子传输

在准理想的色散管理系统中建立了非均匀扰动模型,研究了它们对孤子传输和相互作用的影响.这些扰动导致孤子崩塌,加剧了孤子间相互作用.它们影响的大小与周期长度和扰动强度有关,并且存在最坏周期长度和扰动共振现像.最后,引入非线性增益和滤波器来有效控制这些扰动的影响.     

Effects of correlated perturbations on dark soliton propagation and interaction

Correlated perturbations are considered in a dark soliton system, and their effects on soliton propagation and interaction are investigated numerically. These perturbations result in large sidebands, lead to submergence of dark soliton, and enhance the interaction. The correlation amplifies these effects and shortens the distance until submergence. The comparison of the distinction is made between the degradations of these effects on dark soliton and the corresponding bright soliton. It is found that these effects on dark soliton are less than those on bright soliton. Finally the nonlinear gain is introduced to suppress efficiently these effects.     

Dark soliton interaction in optical time division multiplexed system with randomly varying birefringence and random dispersion map

Correlated perturbations caused by both randomly varying birefringence and random dispersion map are considered in optical time division multiplexed dispersion-managed dark soliton system, and their effects on soliton interaction are investigated numerically. These perturbations enhance soliton interaction, and their effects relate to the strength of perturbation, separation, and pulse width. The correlation plays an important role and reinforces these effects. Moreover, there is a stochastic limit between two perturbations in the system, where the effect is the largest and the corresponding interaction distance is the shortest.     

Effects of Periodically Inhomogeneous Birefringence on Dark-Bright Vector Soliton Propagation and Interaction

The effects of periodically inhomogeneous birefringence on dark-bright vector soliton propagation and interaction are investigated by the numerical method. The birefringence leads to the submergence of the dark soliton and the disintegration of the bright soliton, and enhances the interaction between the neighbouring solitons. The system performance is determined by the bright soliton because the dark soliton has robust features. Finally, the avoidance and the effective control are introduced, and the controlling mechanism is demonstrated.     

Stochastic perturbation in quasi—ideal dispersion—managed soliton system

The model of stochastic perturbation is built up systematically in quasi-ideal dispersion-managed soliton system,its influence on soliton propagation is investigated by both the variational approach and the numerical simulation,and it is found that the stochastic perturbation leads to disintegration of soliton and enhances the interaction between solitons.The nonlinear gain and filter are introduced to suppress effectively the influence on both soliton propagation and interaction.     

Effects of varying nonlocality on dynamics of two-component vector spatial solitons

The randomly and the periodically varying weak nonlocalities are investigated by the variational approach in the self-focusing nonlinear media, and their effects are analyzed on the propagation and interaction of the two-component spatial solitons. The results show that they lead to the soliton disintegration and enhance the interaction between the spatial solitons, and their effects depend on the fluctuation strength and the period length of the varying nonlocalities. Finally, the numerical results confirm the theoretical findings.     

受扰动的光纤孤子间的相互作用

基于含扰动的非线性薛定谔方程，发展了高登的光孤子相互作用理论，直接从近似的二孤子解昨到描述实际光纤通讯中孤子间的相互作用的解析公式，公式表明在实际的通讯系统中光纤孤子间的相互作用不令依赖于它们之间相对相差，而且依赖于它们的相对能量，速度差随传输距离的变化。     

Collision of optical solitons with Kerr law nonlinearity

The intra-channel collision of optical solitons, with Kerr law nonlinearity, is studied by the aid of quasi-particle theory. The perturbation terms considered in this paper are all of Hamiltonian type. It is shown that the soliton–soliton interaction can be suppressed in the presence of these perturbations, namely, the self-steepening, the third-order dispersion, the fourth-order dispersion and the frequency separation between the soliton carrier and the gain-center frequency. The prediction of quasi-particle theory are fully confirmed by direct numerical simulations.     

色散控制光孤子系统性能分析

研究色散控制光孤子系统中的放大器的自发辐射噪声与交叉相位调制对孤子传输特性的影响，采用变分法分析了色散控制孤子的均方频移、定时抖动和误码特性，从降低自发辐射噪声和交叉相位调制扰动引起的均方频移出发，确定了补偿段的特性参量，给出了三种传输控制方案，分析了各方案中色散控制孤子的传输特性，其结果对色散控制孤子系统的设计具有参考价值。     

Finite-Wavelength Stability¶of Capillary-Gravity Solitary Waves

We consider the Euler equations describing nonlinear waves on the free surface of a two-dimensional inviscid, irrotational fluid layer of finite depth. For large surface tension, Bond number larger than 1/3, and Froude number close to 1, the system possesses a one-parameter family of small-amplitude, traveling solitary wave solutions. We show that these solitary waves are spectrally stable with respect to perturbations of finite wave-number. In particular, we exclude possible unstable eigenvalues of the linearization at the soliton in the long-wavelength regime, corresponding to small frequency, and unstable eigenvalues with finite but bounded frequency, arising from non-adiabatic interaction of the infinite-wavelength soliton with finite-wavelength perturbations. Received: 7 February 2001 / Accepted: 6 October 2001     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

主客体式光折变聚合物中空间明孤子的动态演化特性

研究了主客体式光折变聚合物中空间明孤子的动态演化特性,讨论了振幅微扰和宽度微扰对其传播特性的影响.结果表明,入射波为明孤子波时,能够在聚合物中稳定直线传播 在较小微扰情况下,孤子波经短距离传播后能够演化为明孤子波 当微扰比较大时,光波不能在聚合物中稳定传播,而是呈现周期性震荡现象 关键词： 光折变效应 光折变聚合物 空间孤子     

Soliton Perturbations of the Modified Korteweg de Vries Equation

The soliton perturbations of the modified Korteweg de Vries equation corresponding to different signs of the nonlinear term are studied. The first-order effects of perturbation on a soliton, namely, both the slow time-dependence of the soliton parameters and first-order corrections are derived in a direct approach based on the separation of variables.     

Stability of Peakons for an Integrable Modified Camassa-Holm Equation with Cubic Nonlinearity

Considered herein is the dynamical stability of the single peaked soliton and periodic peaked soliton for an integrable modified Camassa-Holm equation with cubic nonlinearity. The equation is known to admit a single peaked soliton and multi-peakon solutions, and is shown here to possess a periodic peaked soliton. By constructing certain Lyapunov functionals, it is demonstrated that the shapes of these waves are stable under small perturbations in the energy space.     

Intra-channel collision of parabolic law optical solitons

The intra-channel collision of optical solitons, with parabolic law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are the nonlinear gain and saturable amplifiers along with filters. The suppression of soliton–soliton interaction, in presence of these perturbations terms, is achieved. The numerical simulations support the quasi-particle theory.     

Family of multi-hump solitons propagating in dispersion-managed optical fiber transmission system and their existent parameter ranges

Multi-hump soliton which consists of plural pulses can propagate in a dispersion-managed optical fiber transmission system with maintaining the pulse-to-pulse spacings. In this paper, the family members of multi-hump soliton are systematically introduced using a family tree. The system parameter ranges in which multi-hump soliton can exist are studied by a numerical averaging scheme. The dependency of pulse energy and pulse-to-pulse spacing on the system parameter is also investigated to show the robustness of anti-phase bi-soliton against imposed perturbations.     

Structures and Interactions of Soliton in (2+1)-Dimensional Generalized Nizhnik-Novikov-Veselov Equation

A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The interactions between a line soliton and a y-periodic soliton are classified into several types according to the phase shifts due to collision. There are two types of singular interactions. One is the resonant interaction that generates one line soliton while the other is the extremely repulsive or long-range interaction where two solitons interchange each other infinitely apart. Some new phenomena of interaction between two dromions are also reported in this paper, and detailed behaviors of interactions are illustrated both analytically and graphically.     

Controlling soliton explosions

We investigate the dynamics of solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and numerically) that some space-dependent perturbations or nonlinear damping can make the soliton internal mode unstable leading to soliton explosion. We will show that, in some cases, while some conditions are satisfied, the soliton explodes becoming a permanent, extremely complex, spatiotemporal dynamics. We believe these mechanisms can explain some of the phenomena that recently have been reported to occur in excitable media. We present a method for controlling soliton explosions.     

The lifetime of the soliton in the improved Davydov model at the biological temperature 300 K for protein molecules

We study the effects of quantum fluctuations and thermal perturbations on the lifetime of the soliton in the improved Davydov model proposed by us with two-quanta and with an added interaction. By using quantum perturbation theory, we compute the soliton lifetime for a wide ranges of parameter values relevant for protein molecules. The lifetime of the new soliton at the biological temperature 300 K is of the order of 10^-10 second or τ/τ≥ 500 for parameters appropriate to α-helical protein molecules. This shows clearly that the new soliton in the improved model is a viable mechanism for the bio-energy transport in the α-helix region of proteins. Received 7 January 1999 and Received in final form 16 August 2000