Impact of Viscosity on DNA Dynamics

We study the influence of viscosity on DNA dynamics. By employing the nonlinear Peyrard-Bishop-Dauxois （PBD） model, it is shown that the DNA dynamics can be explained by a solution of a complex nonlinear Schrǒdinger equation （CNLSE）. This is the nonlinear Schrǒdinger equation （NLSE） with a nonlinear parameter being a complex number. We compare real and imaginary parts of this nonlinear parameter and show that the latter one should not be negligible, which means that the CNLSE should be solved numerically,     

Light-controlled helical pitch and dynamic gratings

A chiral nematic liquid crystal (LC) with a photo-sensitive chiral agent is employed for a light-controlled modulation of optical activity and used as a model substance for a dynamic diffraction grating recording. The described liquid crystalline system has shown a strong nonlinear response with effective parameter of cubic nonlinearity being much greater of that characteristic of the orientational nonlinearity of LC. A simple mathematical model of light diffraction on the grating of modulated optical activity was developed. Calculated values of intensities and polarisation states of diffracting beams have shown very good agreement with the experimental data. LC systems with light-controlled chirality could be promising media for nonlinear optical applications or all-optical switching devices.     

手征参数对光纤中模式特性的影响

对圆芯和包层都是手征介质的阶跃型手征光纤进行了解析求解，导出了模式特征方程，给出了手征光纤中模式场，光强和光功率分布的表达式。分别研究了纤芯和包层中的手征参数对模式特性的影响．。     

非线性偏振旋转锁模自相似脉冲光纤激光器的研究

利用耦合非线性薛定谔方程（CNLSE）为非线性偏振旋转（NPE）锁模自相似光纤激光器建立了一种新的数值模型.模型中,用CNLSE描述脉冲在单模光纤中的传播,在增益光纤中同时考虑了增益带宽和增益饱和作用,用传输矩阵描述构成NPE锁模的光学元件.优化了腔内净色散和光纤长度等参数,模拟了脉冲在激光腔内的演化特性,得到了典型的自相似脉冲运行区域及特点.在最佳自相似脉冲运行区域内,得到了能量约为7 nJ、脉宽约11 ps、线性啁啾的抛物脉冲.比较了不同腔内净色散条件下输出脉冲的特点,给出了三阶色散对输出脉冲的影响. 关键词： 自相似脉冲 非线性偏振旋转锁模 耦合非线性薛定谔方程 数值模拟     

单模手征光纤研究

对圆芯和内外包层都为手征介质构成的双包层手征光纤（W型）进行了解求解,导出了模式场解及模式特征方程,然后用数值计算的方法研究了手征参数对模式的色散曲线和截止频率的影响,结果发现在双包层光纤的纤芯中引入手征或在单包层光纤的包层中引入手征,都可以实现单模工作。     

Spatiotemporal Self-Similar Solutions of the Generalized (3+1)-dimensional Nonlinear Schrödinger Equation with Polynomial Nonlinearity of Arbitrary Order

We construct analytical self-similar solutions for the generalized (3+1)-dimensional nonlinear Schrödinger equation with polynomial nonlinearity of arbitrary order. As an example, we list self-similar solutions of quintic nonlinear Schrödinger equation with distributed dispersion and distributed linear gain, including bright similariton solution, fractional and combined Jacobian elliptic function solutions. Moreover, we discuss self-similar evolutional dynamic behaviors of these solutions in the dispersion decreasing fiber and the periodic distributed amplification system.     

Optical Solitonlike Pulses for Nonlinear Schrödinger Equation with Variable Coefficients

The generalized form with varying coefficients for nonlinear Schrödinger equation including fourth-order dispersion and quintic nonlinearity is presented in this article. The exact bright, dark, and combined solitonlike solutions were given by taking proper ansatz into account. The different forms of dispersion functions were considered to investigate the pulse's evolution or dispersion managements in optical fiber.     

On the conformable nonlinear schrödinger equation with second order spatiotemporal and group velocity dispersion coefficients

In this paper, exact traveling wave solutions of the conformable differential equations have been examined. By means of the wave transformation and properties of the conformable derivative (CD), conformable nonlinear Schrödinger equation (CNLSE) has been converted into an integer order differential equation. To extract optical solutions, the wave profile has been divided into amplitude and phase components. A new extension of the Bäcklund method has been offered and applied to the CNLSE which has important applications in quantum mechanics. Some novel exact traveling wave solutions to the CNLSE with group velocity dispersion and second order spatiotemporal dispersion coefficients are successfully obtained by means of this method.     

Hurst exponents for interacting random walkers obeying nonlinear Fokker-Planck equations

Anomalous diffusion of random walks has been extensively studied for the case of non-interacting particles. Here we study the evolution of nonlinear partial differential equations by interpreting them as Fokker-Planck equations arising from interactions among random walkers. We extend the formalism of generalized Hurst exponents to the study of nonlinear evolution equations and apply it to several illustrative examples. They include an analytically solvable case of a nonlinear diffusion constant and three nonlinear equations which are not analytically solvable: the usual Fisher equation which contains a quadratic nonlinearity, a generalization of the Fisher equation with density-dependent diffusion constant, and the Nagumo equation which incorporates a cubic rather than a quadratic nonlinearity. We estimate the generalized Hurst exponents.     

Optical solitons and optical rogons of generalized resonant dispersive nonlinear Schrödinger's equation with power law nonlinearity

This paper obtains solitons and singular periodic solutions to the generalized resonant dispersive nonlinear Schrödinger’ equation with power law nonlinearity. There are several integration tools that are adopted to extract these solutions. They are simplest equation method, functional variable method, sine–cosine function method, tanh function method and the G′/G-expansion method. These integration techniques reveal bright and singular solitons as well as the corresponding singular periodic solutions to the nonlinear evolution equation. These solitons solutions are important in the nonlinear fiber optics community as well as in the study of rogue waves.     

Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg-Landau equation with variable coefficients

We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically.     

Generalized pohlmeyer transformation — Some nonlinear systems with exponential interactions

The Pohlmeyer transformation between the O(3) nonlinear σ-model and the sine-Gordon equation is generalized to the case of the chiral model on a Kähler manifold. As a result nonlinear systems with the exponential interactions are obtained. Solutions of these systems are derived from solutions of the initial chiral model.     

Dispersion and frequency dependent nonlinearity parameters in a graphite-epoxy composite

Longitudinal phase velocity and nonlinearity parameter have been measured as a function of frequency in the low megaHertz range in a laminate graphite-fiber-epoxy-resin composite. Amplitudes of both the fundamental and generated second harmonics were measured absolutely with a capacitive receiver. Phase velocity and nonlinearity parameter vary with frequency. The extent of the variance depends on the orientation of the fiber layers. Comparison is made between the nonlinear differential equation appropriate for crystals and a new equation that accounts for frequency dependence of phase velocity and nonlinearity parameter. The newer equation describes the data more accurately than the crystalline model does, but appears to require additional terms.     

Analytic investigation on the similariton transmission control in the dispersion decreasing fiber

By means of the similarity transformation, we discuss the generalized nonlinear Schrödinger equation exhibiting inhomogeneous dispersion, nonlinearity and gain or loss at the same time. Explicit bright and dark multi-similariton solutions are obtained. Based on them, we investigate transmission control using the dispersion decreasing fiber with potential applications to the design of high-speed optical devices and amplifiers and pulse compressors, and the development of tunable sources of amplitude modulated light.     

五阶非线性作用下光纤中类明孤子运动方程的变分研究

当考虑到五阶非线性对光脉冲传输的影响时, 光纤中类明孤子的传输服从含五阶非线性修正项的非线性Schrdinger方程。利用何氏半反推法建立该类明孤子运动方程的变分形式, 然后应用何氏变分法导出该方程基态孤子解的双曲正割表达式。同时, 受何氏指数函数方法的启发, 建立了一种新的高斯表达式。一方面, 基于得到的显式表达式相关学者可进一步研究五阶非线性对光脉冲传输的影响。另一方面, 该求解过程也进一步显示了用何氏变分法求解数学物理中非线性发展方程的简洁有效性。     

数值模拟高阶色散和非线性对光孤子传输的影响

光孤子传输中的高阶色散以及高次非线性效应是光纤通讯发展的重要制约因素。从光孤子在光纤中的一般传输方程出发, 在较大的入纤功率的前提下, 综合考虑了高阶色散、五次非线性和损耗因素, 得到其具体传输方程, 并据此从理论上分析了高阶色散和非线性对光孤子传输性能的影响。本文采用分步傅里叶方法, 以MATLAB为实现工具, 实现高阶色散和非线性对光孤子传输影响的模拟计算, 并深入分析了高阶色散和非线性导致的孤子脉冲频移现象。计算结果表明: 在入射功率较大的时候, 高阶色散效应不可忽略。当五次非线性γ2>0时,孤子脉冲主峰发生微小频移; 而当五次非线性γ2<0时, 孤子脉冲主峰基座产生微小频移; 当高阶色散β3>0时频率出现红移, 而当β3<0时, 频率出现蓝移。     

光纤中单光子传输方程的求解及分析

量子信息在光纤中传输时,会受到光纤损耗、色散、非线性效应等多因素的影响,将产生传输态的演化与能量转移.本文以单模光纤传输方程以及电磁场量子化理论为基础,对单模光纤中基模模场进行量子化处理,推导并建立了考虑损耗、色散、非线性效应后的单光子传输方程.基于微扰法对单光子非线性传输方程进行了求解,给出了稳定解存在的必要条件及其所满足的色散方程.深入讨论了广域光功率随微扰频率的变化关系,并且分析了光纤色散、非线性效应对解的影响.为量子光纤传输系统性能的深入研究奠定了理论基础.     

Polarization characteristics of chiral photonic crystal fibers with an elliptical hollow core

The theoretical study of dielectric-chiral photonic crystal fiber(PCF)with an elliptical hollow core is presented.The band structure of chiral photonic crystal(PhC)is calculated by using a modified plane-wave expansion(PWE)method.By examining the out-of-plane photonic bandgaps(PBGs)of chiral PhC,a kind of chiral PCF with a hollow core is designed and their eigenstates are calculated.The distributions of mode field and polarization state are demonstrated,and how the structural asymmetry of the core together with the chirality in the background affects the modal polarization is discussed.The dependences of birefringence on chirality for different ellipticities of core are investigated.     

Guided and surface modes in chiral nihility fiber

Guided and surface modes in the chiral nihility fiber consisting of a chiral nihility metamaterial core with an achiral cladding have been investigated. The dispersion equations of guided and surface modes in the chiral nihility fiber and their cutoff frequencies are derived. Dispersion curves of guided and surface modes are presented and the effect of chirality parameter on dispersion curves is discussed in detail. Some novel propagation characteristics are found.     

Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach

The dynamics of nonlinear pulse propagation in an average dispersion-managed soliton system is governed by a constant coefficient nonlinear Schrödinger (NLS) equation. For a special set of parameters the constant coefficient NLS equation is completely integrable. The same constant coefficient NLS equation is also applicable to optical fiber systems with phase modulation or pulse compression. We also investigate MI arising in the cubic-quintic nonlinear Schrödinger equation for ultrashort pulse propagation. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulation perturbations. Analyzing the ensuing ODE’s, we derive the classical modulational instability criterion and identify it numerically. We show that the quintic nonlinearity can be essential for the stability of solutions. The evolutions of modulational instability are numerically investigated and the effects of the quintic nonlinearity on the evolutions are examined. Numerical simulations demonstrate the validity of the analytical predictions.