Intermittencies in complex Ginzburg-Landau equation by varying system size

Dynamical behaviour of the one-dimensional complex Ginzburg--Landau equation (CGLE) with finite system size $L$ is investigated, based on numerical simulations. By varying the system size and keeping other system parameters in the defect turbulence region (defect turbulence in large $L$ limit), a number of intermittencies new for the CGLE system are observed in the processes of pattern formations and transitions while the system dynamics varies from a homogeneous periodic oscillation to strong defect turbulence.     

Interactions between optical bullets with different velocities in the three-dimensional cubic-quintic complex Ginzburg-Landau equation

By using the three-dimensional complex Ginzburg--Landau equation with cubic--quintic nonlinearity, this paper numerically investigates the interactions between optical bullets with different velocities in a dissipative system. The results reveal an abundance of interesting behaviours relating to the velocities of bullets: merging of the optical bullets into a single one at small velocities; periodic collisions at large velocities and disappearance of two bullets after several collisions in an intermediate region of velocity. Finally, it also reports that an extra bullet derives from the collision of optical bullets when optical bullets are at small velocities but with high energies.     

Stationary patterns in a discrete bistable reaction--diffusion system: mode analysis

This paper theoretically analyses and studies stationary patterns in diffusively coupled bistable elements. Since these stationary patterns consist of two types of stationary mode structure: kink and pulse, a mode analysis method is proposed to approximate the solutions of these localized basic modes and to analyse their stabilities. Using this method, it reconstructs the whole stationary patterns. The cellular mode structures (kink and pulse) in bistable media fundamentally differ from stationary patterns in monostable media showing spatial periodicity induced by a diffusive Turing bifurcation.     

Amplitude wave in one-dimensional complex Ginzburgben Landau equation

The wave propagation in the one-dimensional complex Ginzburg-Landau equation (CGLE) is studied by considering a wave source at the system boundary. A special propagation region, which is an island-shaped zone surrounded by the defect turbulence in the system parameter space, is observed in our numerical experiment. The wave signal spreads in the whole space with a novel amplitude wave pattern in the area. The relevant factors of the pattern formation, such as the wave speed, the maximum propagating distance and the oscillatory frequency, are studied in detail. The stability and the generality of the region are testified by adopting various initial conditions. This finding of the amplitude pattern extends the wave propagation region in the parameter space and presents a new signal transmission mode, and is therefore expected to be of much importance.     

The complex multi-symplectic scheme for the generalized sinh-Gordon equation

In this paper,the complex multi-symplectic method and the implementation of the generalized sinhGordon equation are investigated in detail.The multi-symplectic formulations of the generalized sinh-Gordon equation in Hamiltonian space are presented firstly.The complex method is introduced and a complex semi-implicit scheme with several discrete conservation laws(including a multi-symplectic conservation law(CLS),a local energy conservation law(ECL) as well as a local momentum conservation law(MCL)) is constr...     

Conservation laws of the complex short pulse equation and coupled complex short pulse equations

In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases. Based on the linearizing operator and adjoint linearizing operator for the two real systems, adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair (SA) method. Relationships between the nonlinear self-adjointness method and the SA method are investigated.     

耦合复金兹堡-朗道(Ginzburg-Landau)方程中的模螺旋波

以双层耦合复金兹堡-朗道(Ginzburg-Landau)方程系统为时空模型, 研究了其中的模螺旋波, 讨论了这种特殊波动现象的稳定条件和相关影响因素. 模螺旋波与该类时空系统中常见的相螺旋波相比, 其中心不存在缺陷点, 同时仅在其变量的振幅部分(而非相位部分) 表现为螺旋结构. 本文通过数值方法研究了耦合复金兹堡-朗道方程中产生模螺旋波所需要的初始和参数条件.研究表明, 当双层耦合系统的初始斑图之间的差距较大时, 才能够产生模螺旋波; 同时观察到系统在参数不匹配的条件下会发生相螺旋波向模螺旋波的转变.通过对同步函数的计算, 发现该转变过程具有非连续性.     

Direct perturbation method for perturbed complex Burgers equation

So far, Lou's direct perturbation method has been applied successfully to solve the nonlinear Schr?dinger equation(NLSE) hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. But to our knowledge, this method for other types of perturbed nonlinear evolution equations has still been lacking. In this paper, Lou's direct perturbation method is applied to the study of perturbed complex Burgers equation. By this method, we calculate not only the zero-order adiabatic solution, but also the first order modification.     

复Ginzburg-Landau方程中模螺旋波的稳定性研究

研究了复Ginzburg-Landau方程系统中模螺旋波与其他斑图在同一平面内的竞争行为,发现演化结果在系统参数平面内可分为四个主要区域:在I区和III区中,模螺旋波与相螺旋波相比稳定性较差,模螺旋波的空间被相螺旋波所入侵.在II区中,模螺旋波具有较强的稳定性,相螺旋波的空间被模螺旋波所入侵.在IV区内,由于时空混沌所导致的频率不稳定性,演化的结果较为复杂.我们通过对模螺旋波、相螺旋波以及时空混沌的频率分析,发现当模螺旋波的系统参数为α1=-1.34,β1=0.35时,较高频率的模螺旋波具有较好的稳定性,高频模螺旋波可以入侵低频斑图空间.竞争结果主要受系统变量实部的频率影响,频率分析所得到的理论结果与数值实验结果符合得非常好.     

A new pseudorandom number generator based on complex number chaotic equation

In recent years, various chaotic equation based pseudorandom number generators have been proposed, however, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandom number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.     

Stability of dark soliton solutions of the quintic complex Ginzburg--Landau equation inthe case of normal dispersion

Dark soliton solutions of the one-dimensional complex Ginzburg--Landau equation (CGLE) are analysed for the case of normal group-velocity dispersion. The CGLE can be transformed to the nonlinear Schr\"{o}dinger equation (NLSE) with perturbation terms under some practical conditions. The main properties of dark solitons are analysed by applying the direct perturbation theory of the NLSE. The results obtained may be helpful for the research on the optical soliton transmission system.     

A new pseudorandom number generator based on a complex number chaotic equation

In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandom number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.     

基于复Ginzburg-Landau方程的双核光纤中调制不稳定性的仿真研究

在双核光纤光学系统中,应用复Ginzburg-Landau方程,研究了连续波的不稳定性问题.双核光纤光学系统是由一个非线性离散主核和一个线性附核构成的.研究发现,在线性微扰下存在调制不稳定性.系统仿真结果表明：如果充分考虑调制不稳定性,则该系统将产生规则或者不规则的脉冲序列.反之,如果不考虑调制不稳定性它将产生一连串具有连续增长振幅的离散峰.这表明在反常群速度色散情况下,一串归零脉冲的峰值或者单一归零脉冲峰值仍然是增强的.在光纤中产生归零序列脉冲源,这一研究结果对全光纤通信有一定的价值,对光纤光学及物理学 关键词： 光孤子 复Ginzburg-Landau方程 双核光纤 调制不稳定性     

Relation between the Kähler equation and the Dirac equation

The formal analogy and the substantial differences between the Kähler equation and the Dirac equation are explained in terms of the relativistic compatibility of a common differential operator on the Clifford algebraC with two distinct representations of the Lorentz Lie algebra onC.     

Circulation system complex networks and teleconnections

In terms of the characteristic topology parameters of climate complex networks, the spatial connection structural complexity of the circulation system and the influence of four teleconnection patterns are quantitatively described. Results of node degrees for the Northern Hemisphere (NH) mid-high latitude (30^circ N—90^circ N) circulation system (NHS) networks with and without the Arctic Oscillations (AO), the North Atlantic Oscillations (NAO) and the Pacific—North American pattern (PNA) demonstrate that the teleconnections greatly shorten the mean shortest path length of the networks, thus being advantageous to the rapid transfer of local fluctuation information over the network and to the stability of the NHS. The impact of the AO on the NHS connection structure is most important and the impact of the NAO is the next important. The PNA is a relatively independent teleconnection, and its role in the NHS is mainly manifested in the connection between the NHS and the tropical circulation system (TRS). As to the Southern Hemisphere mid-high latitude (30^circ S—90^circ S) circulation system (SHS), the impact of the Antarctic Arctic Oscillations (AAO) on the structural stability of the system is most important. In addition, there might be a stable correlation dipole (AACD) in the SHS, which also has important influence on the structure of the SHS networks.     

Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M-dimensional loop algebra \tilde{X} is produced. By taking advantage of \tilde{X}, a new isospectral problem is established and then by making use of the Tu scheme the multi-component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra \tilde{F}_M of the loop algebra \tilde{X} is presented. Based on the \tilde{F}_M, the multi-component integrable coupling system of the multi-component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.     

Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system

In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz-Ladik-Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz-Ladik-Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz-Ladik-Lattice method is verified.     

(2+1)维色散长波方程的新精确解及其复合波激发

利用Riccati方程展开法和变量分离法,得到了(2+1)维色散长波方程的变量分离解.根据得到的孤波解,构造出该方程新颖的复合波局域结构,研究了复合波随时间的演化.     

Numerical simulation of the soliton solutions for a complex modified Korteweg—de Vries equation by a finite difference method

In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance.     

Dispersion equation of a double shell-fluid coupled system

I.IntroductionInadditiontofluid-filledductsofcylindrica1cross-sections,theannu1arcross-sectionductshavebeenalsowidelyusedinmanyindustrialanddefenseapplicationsduetotheirspecialdemands.SuchconfigurationsarefrequentIyfoundinheatexchangers,certaindesignsofnuclearreactors,largejetpumps,aircraftengines,andsoon.Inapowerplant,theair-cooledbusbar,whichisappliedfOrconnectionofe1ectricgeneratorwithtransformers,isalsoanexamp1eofengineeringapplicationsinvolvingsuchgeometries.Manyvitalcomponentsofanuclea…