Perturbation theory for the double sine-Gordon equation

This paper presents a perturbation theory for the double sine-Gordon equation. We obtain a system of differential equations that shows the soliton parameters modification under the influence of the perturbation. For the particular case λ=0 the results transform into the well-known perturbation theory for the sine-Gordon equation.     

Simulations of rare events in fiber optics by interacting particle systems

In this paper we study the robustness of linear pulses, solitons, and dispersion-managed solitons, under the influence of random perturbations. First, we address the problem of the estimation of the outage probability due to polarization-mode dispersion. Second, we compare the pulse broadening due to random fluctuations of the group-velocity dispersion. We use an original interacting particle system to estimate the tails of the probability density functions of the pulse widths. A new adaptative Monte Carlo method is applied that enforces the simulations to probe the regions of practical importance by selection and mutation steps.     

双函数法及一类非线性发展方程的精确行波解

给出一种求解非线性发展方程精确行波解的新方法：双函数法。使用此方法，获得了一类非线性发展方程的许多精确行波解，其中包括孤波解和周期解，推广了文献用其它方法取得的结果，同时还获得了许多新的弧波解和周期解，借助于Mathemat-ica，此方法能部分地在计算机上实现。     

强双折射光纤中暗孤子的传输特性研究

从光纤双折射参量、背景光宽度、孤子脉冲宽度三方面探讨暗孤子在双折射光纤中远距离传输特性研究表明:相对于亮孤子,暗孤子对光纤双折射的自适应能力较弱;背景光宽度越大,暗脉冲与背景光对比度越好,暗孤子越能保持原来黑孤子状态;暗孤子脉冲宽度越大,偏振脉冲之间的差分群时延越大,诱导的灰孤子震荡结构越明显,越不利于暗孤子远距离传输.     

The negative extended KdV equation with self-consistent sources: soliton, positon and negaton

The negative extended KdV equation with self-consistent sources (eKdV⁻ESCSs) is firstly presented and the associated linear auxiliary equations are derived. The generalized binary Darboux transformation (DT) is applied to construct some new solutions of the eKdV⁻ESCSs such as singular N-soliton solution, N-soliton solution with finite amplitude, N-positon solution and N-negaton solution. The properties of these solutions are analyzed. Moreover, the interactions of two solitons, positon and negaton, positon and soliton, and two positons are discussed.     

On the periodic solutions for both nonlinear differential and difference equations: A unified approach

A direct and unifying scheme for disclosure of periodic wave solutions of both nonlinear differential and difference equations is presented. The scheme is based on Hirota's bilinear form and certain Riemann theta function formulae. The relations between the periodic wave solutions and soliton solutions are rigorously established.     

Time-reversal symmetry-breaking in two-band superconductors

Competition between an interband Josephson interaction and a biquadratic interband interaction can break time-reversal symmetry when the interband interactions are very weak compared with the intraband interaction. We demonstrate this using the phenomenological Ginzburg–Landau free energy, taking into account terms essential for this phenomenon. This time-reversal symmetry-breaking state peels away a sheet of an interband phase difference soliton wall. This sheet is the domain wall between two different chiral states. The peeling reduces the formation energy of the domain wall. The domain wall can simultaneously erase the Meissner effect and the specific heat jump when the entropy invokes many domain walls, and its life time is prolonged by a pinning owing to an inhomogeneity such as surface roughness.     

Periodic intensity variations on the pulse-train of a passively mode-locked fiber ring laser

We investigate the evolvement of the periodic intensity variations of the pulse-train in a fiber ring laser mode-locked by the nonlinear polarization rotation technique. It is found that the phenomenon of such intensity fluctuations is related to the orientation of the polarization controllers when the pump power is fixed. The numerical results show that the mechanism of the periodic intensity variations is caused by the interaction of the nonlinear polarization rotation and the passive polarizer in the cavity.     

Gaussian soliton generation using a 1.3 μm optical pulse in a micro-ring resonator for a new DWDM enhancement

We present a novel system of a Gaussian soliton generation using a 1.30 μm optical pulse in a nonlinear micro-ring resonator system, which can be used to form the soliton pulse trains within the new wavelength band. By using the suitable parameters, the soliton pulse trains with the center wavelength at 1.30 μm can be generated after the intense Gaussian pulse is input into the nonlinear micro-ring resonator system. The initial pulse bandwidth is enlarged and the signal amplified by the nonlinear Kerr effects type within the ring resonator. The simulation values are used associating with the practical device parameters, whereas the obtained results have shown that the wavelength enhancement of the center wavelength can be achieved. Furthermore, the maximum soliton output power of 12 W is obtained, which is available to perform the long-distance communication link. The common problem of soliton dispersion is minimized by the zero dispersion condition in this case. The major advantage of the proposed system is that the dense wavelength division of the center wavelength with the spectral width of 7.0 pm (10⁻¹⁵ m) and the free spectrum range of 400 pm can be generated and achieved. This is available for the used/installed wavelength enhancement, which can provide more available channel capacity in the existed public optical network.     

Nonlinear spin excitations in a classical Heisenberg anisotropic helimagnet

The nonlinear spin excitations in an anisotropic helimagnet in the presence of a constant magnetic field are investigated in the classical continuum limit. The helical character is introduced into the model, in analogy with the twist in a cholesteric liquid crystal. After deriving a class of spin wave solutions for the stereographic representation of the Landau-Lifshitz equation, in-plane stationary spin configurations are obtained and their stability is analysed. When the external magnetic field is along the anisotropic axis, modulational instability is observed in the spin lattice, and when the external magnetic field is normal to the anisotropic axis, the spin configurations are unstable. The perturbed spin components show fluctuations in the tail region, while the velocity and amplitude of the soliton remain unaltered.