New Optical Solitons in High-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

By using the generalized tanh-function method, we find bright and dark solitary wave solutions to an extended nonlinear Schrödinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses. At the same time, we also obtained other types of exact solutions.     

Properties of Controllable Soliton Switching in Optical Lattices with Longitudinal Exponential-Asymptotic Modulation

The properties of controllable soliton switching in Kerr-type optical lattices with different modulation are investigated theoretically and simulated numerically. The results show that the optical lattices can be available for all-optical soliton switching through utilization for length-scale competition effects. And through longitudinal exponential-asymptotic modulation for the linear refractive index, the properties of soliton switching in the optical lattices can be improved. The number of output channels of soliton switching can be controlled by the parameters such as incident angle, asymptotic rate of longitudinal modulation, guiding parameter and form factor.     

Dynamics of Nonautonomous Dark Solitons

We solve a generalized nonautonomous nonlinear Schrdinger equation analytically by performing the Hirota's bilinearization method. The precise expression of a parameter , which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton (∈2≠1) while it has no effects on the wave central position.Moreover, the precise expressions of a nonautonomous black soliton's (∈2≠1) width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton's evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.     

Higher-Order Effects Induced Optical Solitons in Fiber

In this paper, we study the existence conditions of the soliton solutions induced by considering the higher-order effects such as the third-order dispersion (TOD), self-steepening (SS), and self-frequency shift arising from stimulated Raman scattering (SRS) simultaneously in optical soliton communication. Based on the Jacobian expansion method, we successfully obtain bright and dark solitons. The results shows that the resultant inclusion is in agreement with Mollenauer et al. [Physical Review Letters 45 (1980) 1095] when the SRS is not considered; while when the SRS is considered, the existence conditions of the higher-order effects induced bright and dark solitons are not only quite different from those of the group velocity dispersion (GVD)-induced and self-phase modulation (SPM)-induced solitons, but also different from those of the TOD- and SS-induced solitons discussed by Mollenauer et al. [Physical Review Letters 45 (1980) 1095].     

Pulse Amplification in Dispersion-Decreasing Fibers with Symbolic Computation

The pulse amplification in the dispersion-decreasing fiber (DDF) isinvestigated via symbolic computation to solve the variable-coefficient higher-order nonlinear Schrödinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering. The analytic one-soliton solution of this model is obtained with a set of parametricconditions. Based on this solution, the fundamental soliton is shown to be amplified in the DDF. The comparison of the amplitude of pulses for different dispersion profiles of the DDF is also performed through the graphical analysis. The results of this paper would be of certain value to the study of signal amplification and pulse compression.     

Double Humped Grey and Black Solitons in Kerr Nonlinear Media

The existence of a new class of double humped grey and dark solitons in a Kerr nonlinear medium has been predicted in this paper. Following well known variational procedure, the dynamics of the propagating soliton has been converted to a Hamiltonian formulation. A set of ordinary differential equations is then derived, which was subsequently examined to predict the existence of double humped grey and dark solitons. Linear stability analysis, numerical appreciation and phase plane dynamics show that these solitons are stable.     

Multi-Solitons and Combined Solitons with Self-Similar Behaviors in a Birefringent Fiber with Higher-Order Effects

A coupled variable-coefficient higher-order nonlinear Schr(o|¨)dinger equation in biretringent fiber is studied,and analytical multi-soliton,combined bright and dark soliton,W-shaped and M-shaped soliton solutions are obtained.Nonlinear tunnelling of these combined solitons in dispersion barrier and dispersion well on an exponential background is discussed,and the decaying or increasing,even lossless tunnelling behaviors of combined solitons are decided by the decaying or increasing parameter.     

Analytical Periodic Wave and Soliton Solutions of the Generalized Nonautonomous Nonlinear Schrödinger Equation in Harmonic and Optical Lattice Potentials

We construct analytical periodic wave and soliton solutions to the generalized nonautonomous nonlinear Schrödinger equation with time- and space-dependent distributed coefficients in harmonic and optical lattice potentials. We utilize the similarity transformation technique to obtain these solutions. Constraints for the dispersion coefficient, the nonlinearity, and the gain (loss) coefficient are presented at the same time. Various shapes of periodic wave and soliton solutions are studied analytically and physically. Stability analysis of the solutions is discussed numerically.     

叶绿素丙酮溶液中热致暗空间光孤子实验

设计了热致暗空间光孤子的实验光路和偶边界条件的实施方案，在叶绿素丙酮溶液中实现了热致暗空间光孤子实验，并采用分步傅里叶变换法进行了数值模拟，发现两者的结果一致。     

Optical Solitons in Fibers for Communication Systems

Abstract

A brief history of attempts to use solitons for optical fiber communications and of the technical developments toward making soliton transmission practical is reviewed. The main problems affecting long-distance soliton transmission, as well as techniques to solve them, are described. Recent developments concerning the use of dispersion management and some of the remarkable properties of dispersion managed solitons are also discussed.     

Optical Solitons in Fibers for Communication Systems

A brief history of attempts to use solitons for optical fiber communications and of the technical developments toward making soliton transmission practical is reviewed. The main problems affecting long-distance soliton transmission, as well as techniques to solve them, are described. Recent developments concerning the use of dispersion management and some of the remarkable properties of dispersion managed solitons are also discussed.     

Soliton and Rogue Wave Solution of the New Nonautonomous Nonlinear Schrödinger Equation

In this paper, a new type (or the second type) of transformation which is used to map the variable coefficient nonlinear Schrödinger (VCNLS) equation to the usual nonlinear Schrödinger (NLS) equation is given. As a special case, a new kind of nonautonomous NLS equation with a t-dependent potential is
introduced. Further, by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation, the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally, through using the new transformation, a new expression, i.e., the non-rational formula, of the rogue wave of a special VCNLS equation is given analytically.
The main differences between the two types of transformation mentioned above are listed by three items.     

On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrödinger Equation for Interdiffused Quantum Wells and Quantum Wires

We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrödinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domain.The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires.Also,the model of a linear harmonic oscillator is considered for comparison reasons.It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range,which is thus considered to be optimal.This range is found to depend on the number of mesh nodes N approximately as α₀ log_e^α₁(α₂ N),where the values of the constants α₀,α₁,and α₂ are determined by fitting the numerical data.And the optimal range is found to be a weak function of the diffusion length.Moreover,it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrödinger equation.     

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。     

Dark Solitons in FPU Lattice Chain

Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.     

Spatial Dark Solitons in an Atom Laser Beam

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Study of Exact Solutions to Cubic-Quintic Nonlinear Schrödinger Equation in Optical Soliton Communication

A systematic method which is based on the classical Lie group reduction is used to find the novel exact solution of the cubic-quintic nonlinear Schrödinger equation (CQNLS) with varying dispersion, nonlinearity, and gain or absorption. Algebraic solitary-wave as well as kink-type solutions in three kinds of optical fibers represented by coefficient varying CQNLS equations are studied in detail. Some new exact solutions of optical solitary wave with a simple analytic form in these models are presented. Appropriate solitary wave solutions are applied to discuss soliton propagation in optical fibres, and the amplification and compression of pulses in optical fibre amplifiers.     

Exact Solutions of Five Complex Nonlinear Schrödinger Equations by Semi-Inverse Variational Principle

In this paper, we establish exact solutions for five complex nonlinear Schrödinger equations. The semi-inverse variational principle (SVP) is used to construct exact soliton solutions of five complex nonlinear Schrödinger equations. Many new families of exact soliton solutions of five complex nonlinear Schrödinger equations are successfully obtained.     

Darboux Transformations,Higher-Order Rational Solitons and Rogue Wave Solutions for a(2+1)-Dimensional Nonlinear Schrdinger Equation

By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a modified KdV equation and an NLS equation. With the help of symbolic computation, some higher-order rational solutions and rogue wave(RW) solutions are constructed by its(1, N-1)-fold DTs according to determinants. From the dynamic behavior of these rogue waves discussed under some selected parameters, we find that the RWs and solitons are demonstrated some interesting structures including the triangle, pentagon, heptagon profiles, etc. Furthermore, we find that the wave structure can be changed from the higher-order RWs into higher-order rational solitons by modulating the main free parameter. These results may give an explanation and prediction for the corresponding dynamical phenomena in some physically relevant systems.     

Series Solution for Localization and Entanglement of an Exciton in a Quantum Dot Molecule by an ac Electric Field

The Schrödinger equation involving the phenomenon of the localization and entanglement for an exciton in a quantum dot molecule by an ac electric field is analytically investigated. New exact series solutions for the Schrödinger equation have been obtained for the first time. The analytical expressions can further describe the dynamical behaviors of an interacting electron-hole pair in a double coupled quantum dot molecule under an ac electric field accurately.