氢键链中的快模与慢模孤子偶

在氢键链二分量模型中，研究质子子晶格和重离子子晶格相互作用项中同时含有非线性耦合和线性耦合两部分的系统，得到快模孤子偶和慢模孤子偶．对于慢模孤子而言，非线性耦合降低了质子子晶格中孤子的有效质量，而线性耦合增加了质子子晶格中孤子的有效质量；对于快模孤子而言，情况正好相反．

高能量掺Yb偏振型大模场面积光子晶体光纤孤子锁模飞秒激光器

实验研究了基于掺Yb偏振型大模场面积光子晶体光纤的孤子锁模激光器,获得了高脉冲能量的飞秒激光输出.激光器基于线形腔结构,利用光栅对补偿腔内色散,并通过半导体可饱和吸收镜实现锁模的自启动.实验中从振荡级直接获得了平均功率为700 mW,重复频率为47.3 MHz(对应于14.8 nJ的单脉冲能量),脉冲宽度为518 fs的稳定锁模脉冲输出.与普通孤子锁模飞秒光纤激光器相比,输出的单脉冲能量提高了两个数量级.

大模场面积光子晶体光纤耗散孤子锁模激光器

研制了一种基于掺Yb3+的双包层大模场面积偏振光子晶体光纤的耗散孤子锁模激光器.利用数值模拟分析了光纤激光器中耗散孤子动力学过程,与全正色散锁模激光器相比,脉冲窄化机理更加丰富,半导体可饱和吸收镜(SESAM)的非线性吸收,啁啾脉冲的光谱滤波以及光纤的增益色散同时起作用,这些因素使耗散孤子锁模更加容易实现,并且稳定运行.其中,光谱滤波的耗散过程是稳定锁模机制的主导因素,滤波片能够在频域和时域同时窄化脉冲,并且去除脉冲啁啾,限制脉冲在腔内始终小于1ps.在实验上实现了无色散补偿腔中直接输出脉冲宽度777fs,最高平均功率达到1W,重复频率48·27MHz,对应单脉冲能量20nJ的飞秒激光.

主动锁模光纤激光器的孤子理论分析

系统考虑了光纤激光器腔构参数与锁模脉冲参数的制约关系 ,建立了完整形式的振幅调制主动锁模光纤激光器的稳态方程 ;据此方程分析了主动锁模光纤激光器腔参数对锁模孤子脉冲参数的影响 ;

具有二阶和三阶非线性一维光子晶体中的耦合模孤子

研究同时具有二阶和三阶非线性的一维光子晶体中的耦合孤子动力学 .从Maxwell方程出发 ,利用多重尺度法 ,导出了光学整流场与两个基频电场包络的非线性耦合模方程组 ,给出了耦合模方程组的孤子解 .结果表明 ,由于二阶非线性导致的光学整流场对基频电场有调制作用 ,使得两个基频电场分量可以呈现为亮孤子 亮孤子、暗孤子 暗孤子及亮孤子 -暗孤子对 ;当两个基频电场的振动频率趋于光子晶体频带的带边频率时 。

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.

~ Transform Demonstration of Dark Soliton Solutions Found by Inverse Scattering

One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.

Features of Motion of Soliton Transported Bio-energy in Aperiodic α-Helix ProteinMolecules with Three Channels

The structure aperiodicities can influence seriously the features of motion of soliton excited in the α-helix protein molecules with three channels. We study the influence of structure aperiodicities on the features of the soliton in the improved model by numerical simulation and Runge-Kulta method. The results obtained show that the new soliton is very robust against the structure aperiodieities including large disorder in the sequence of mass of the amino acids and fluctuations of spring constant, coupling constant, dipole-dipole interactional constant, ground state energy and chain-chain interaction. However, very strong structure aperiodieities can also destroy the stability of the soliton in the α-helix protein molecules.

基于渐变折射率多模光纤的锁模光纤激光器

结合渐变折射率多模光纤的可饱和吸收效应和马赫-曾德尔干涉滤波效应,提出了一种渐变折射率多模光纤-单模光纤-渐变折射率多模光纤(GIMF-SMF-GIMF)结构,在环形掺铒光纤激光器中实现了单波长可调谐和双波长可切换的锁模脉冲运转。基于GIMF-SMF-GIMF的锁模结构,获得的波长可调谐范围为1550.9~1558.9 nm,最短脉冲宽度为0.6 ps。在泵浦功率增加至110 mW时,改变腔内激光的偏振态,实现了中心波长1531.6 nm/1556.2 nm处的单、双波长的可切换锁模激光输出。结果表明,基于GIMF-SMF-SIMF的全光纤结构在掺铒光纤激光器中具有波长可调谐和双波长锁模的潜力,对高速大容量光纤通信系统中的多通道光源的设计具有借鉴意义。

New Multi-soliton Solutions for the (2+1)-Dimensional Kadomtsev-Petviashvili Equation

In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a （1＋1）- dimensional Broer-Kaup （BK） equation and a （1＋1）-dimensional high-order Broer-Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili （KP） equation are obtained.

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect （and also diminished for the linear defocusing effect）. In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through.

Nonlinear Interactions of Dispersion-managed Soliton in OTDM Systems

The dispersion-managed soliton (DMS) transmission model of dispersion-managed systems is established,and the intrachannel DMS interactions equation is obtained.The impact of soliton interactions on DMS systems are numerically investigated.Finally,the relationships of the collision length changing with map strength are revealed.

Soliton, Positon and Negaton Solutions of Extended KdV Equation

Darboux transformation （DT） provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV （eKdV） equation, by which some new solutions such as singular soliton, negaton, and positon solutions are computed for the eKdV equation. We rediscover the soliton solution with finiteamplitude in [A.V. Slyunyaev and E.N. Pelinovskii, J. Exp. Theor. Phys. 89 （1999） 173] and discuss the difference between this soliton and the singular soliton. We clarify the relationship between the exact solutions of the eKdV equation and the spectral parameter. Moreover, the interactions of singular two solitons, positon and negaton, positon and soliton, and two positons are studied in detail.

Statistical characteristics and effects of polarization mode dispersion in dispersion managed soliton systems

Firstly,the JME（Jones matrix eigen） method is used to simulate the statistical characteristics of first- and second-order PMD in dispersion management system. Then,with help of the CNLSE （coupled nonlinear Schrodinger equations） ,the effects of PMD on DMS （dispersion managed soliton） transmission is studied with a variational method. The simplified relationships of the statistical parameters of second-order and first-order of PMD in dispersion management system have been gotten,from which the detailed information of second-order can be obtained, if the condition of DGD is given. The results have shown that the first and second-order PMD （polarization mode dispersion） vectors influence the evolution of energy and Mean square of time displacement of DMS in high-speed bit rates systems. When DPMD^1st〉0.3 ps/km^1/2 ,we must consider some means of control（for example the filter） to restrain the PMD.

Oscillating Solitons for （2＋1）-Dimensional Nonlinear Models

Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.

Cusped Solitons and Loop-Solitons of Reduced Ostrovsky Equation

The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.

Nonlocal Optical Spatial Soliton with a Non-parabolic Symmetry and Real-valued Convolution Response Kernel

Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, Δn2 （I）≈ρ（b0＋ b1f - b2 f^2 with b2/b1 〉 0 is assumed. Furthermore, instead of the wave function Ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If the frequency shift of wave number β satisfies 0 〈 4（β - ρbo/μ） 〈 3η0/8α, the bistable state soliton solution is stable against perturbation. It should be emphasized that the soliton solution arising from a parabolic-symmetry response kernel is trivial. The sufficient condition for the existence of bistable state soliton solution b2/b1〉 0 has been demonstrated.

N-Fold Darboux Transformation and Bidirectional Solitons for Whitham-Broer-Kaup Model in Shallow Water

Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kaup system whose Lax pair can be derived by the Ablowitz-Kaup-Newell-Segur technology. With symbolic computation, based on the aforementioned Lax pair, the N-fold Darboux transformation is constructed with a gauge transformation and the multi-soliton solutions are obtained. Finally, the elastic interactions of the two-soliton solutions (including the head-on and overtaking collisions) for the WBK system are graphically studied. Those multi-soliton collisions can beused to illustrate the bidirectional propagation of the waves in shallow water.

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

A semi-direct sum of two Lie algebras of four-by-four matrices is presented,and a discrete four-by-fourmatrix spectral problem is introduced.A hierarchy of discrete integrable coupling systems is derived.The obtainedintegrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity.Finally,we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discreteHamiltonian systems.

Evolution Property of Multisoliton Excitations for a Higher-Dimensional CoupledBurgers System

By means of the standard truncated Painlevé expansion and a special B?cklund transformation, the higher-dimensional coupled Burgers system (HDCB) is reduced to a linear equation, and an exact multisoliton excitation is derived. The evolution properties of the multisoliton excitation are investigated and some novel features or interesting behaviors are revealed. The results show that after interactions for dromion-dromion, solitoff-solitoff, and solitoff-dromion, they are combined with some new types of localized structures, which are similar to classic particles with completely nonelastic behaviors.