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.     

Two-dimensional coupled mode equation for grating waveguide excitation by a focused beam

The problem of grating coupling of a focused incident beam under non-normal incidence into a slab waveguide is given a complete three-dimensional (3D) solution. The diffracted field is expressed as the Fourier integral of a regular part and of a singular part resulting from the existence of the coupled guided mode. A suitable expression of the field in the neighborhood of the pole and a rigorous definition of the modal field lead to a generalized coupled mode equation relating the incident field and the two-dimensional (2D) modal field propagating in the plane of the slab waveguide. The phenomenological parameters involved in the coupled wave equation: the propagation constant, the radiation coefficient as well as the modal field shape are derived from the exact treatment of plane wave diffraction in the same structure. The solution of the complete coupling problem is given in the particular case of a Gaussian incident beam, and of a high index step-index waveguide.     

Disappearance of laser instabilities in a Gaussian cavity mode

We consider a homogeneously-broadened ring laser with spherical mirrors. We show that if ones assumes a gaussian transverse profile for the electric field, all the instabilities predicted by the plane wave theory vanish. The analysis is performed in the mean field limit, assuming that a suitably defined Fresnel number is much larger than unity and that perfect tuning between atoms and cavity exist.     

Long wavelength instabilities of perfectly square planforms in nonlinear convection

The long wavelength instabilities of square planforms are studied using amplitude equations which describe the general interaction of two orthogonal coupled roll patterns. In addition to the zig-zag, two-dimensional and three-dimensional Eckhaus instabilities, a truly three-dimensional rectangular instability is found. Nonlinear phase diffusion equations are derived close to the onset of the instabilities.University of Gambridge, Gambridge, United Kingdom. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 788–792, August, 1993.     

Approximate analytic solutions for a generalized Hirota—Satsuma coupled KdV equation and a coupled mKdV equation

<正>This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota-Satsuma coupled Korteweg-de Vries(KdV) equation and a coupled modified Korteweg-de Vries(mKdV) equation. This method provides a sequence of functions which converges to the exact solution of the problem and is based on the use of the Lagrange multiplier for the identification of optimal values of parameters in a functional.Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.     

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.     

Modulational instabilities in Josephson oscillations of elongated coupled condensates

We study the Josephson oscillations of two coupled elongated condensates. Linearized calculations show that the oscillating mode uniform over the length of the condensates (uniform Josephson mode) is unstable: modes of non zero longitudinal momentum grow exponentially. In the limit of strong atom interactions, we give scaling laws for the instability time constant and unstable wave vectors. Beyond the linearized approach, numerical calculations show a damped recurrence behavior: the energy in the Josephson mode presents damped oscillations. Finally, we derive conditions on the confinement of the condensates to prevent instabilities.     

Exact solutions to a coupled nonlinear equation

A coupled nonlinear partial differential equation is studied which represents a model for wave propagation in a one-dimensional nonlinear lattice in the absence of one of the variables. The coupled equation is solved exactly by applying the criteria of the Weierstrass elliptic function.     

Convective and absolute instabilities in the subcritical Ginzburg-Landau equation

We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity. Received 17 December 1998     

Finite motion of a particle in coupled quantum wells

We examine the nonstationary state of a particle in two or three coupled quantum wells by introducing quasiseparate potentials. We obtain analytic expressions for the tunneling time and the single-particle quantum current in the WKB approximation. The general result is applied to the case of a triangular barrier.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 87–91, September, 1989.     

Simulation of the resistive state of superconducting films in a magnetic field on the basis of the nonstationary ginzburg-landau equation

By numerical simulation of the temporal two-dimensional Ginzburg-Landau equation, we study the resistive state in superconducting bridges with dimensions ξ ≪ d ≪ λ. It is found that the basis of the resistive state here is, as for d ≫ λ, the vortical structures (vortices) whose motion defines the resistive state. It is shown that the motion of vortices is stochastic in a certain range of currents and magnetic fields. We give a classification of possible dynamic and stochastic modes and examine the transitions from the current flow mode, which is observed for large magnetic fields and small transport currents, to the mode of fast phase slippage. The symmetry breaking effect of the resistive state, which results in cross tension with a quadrupole structure, has been detected. Institute of Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenü, Radiofizika, Vol. 40, Nos. 1–2, pp. 213–231, January–February, 1997.     

Modulation instabilities in a system of four coupled, nonlinear Schrödinger equations

The modulation instability of continuous waves for a system of four coupled nonlinear Schrödinger equations, two of which are in the unstable regime, is studied. In earlier studies, plane or continuous waves for a system of two coupled, nonlinear Schrödinger equations is shown to exhibit modulation instability (MI), even if both modes are in the normal dispersion regime, provided that the coefficient of cross phase modulation (XPM) is larger than that of self phase modulation (SPM). Requirements for MI in this system of four coupled, nonlinear Schrödinger equations can be relaxed. MI can occur even if the magnitude of XPM is less than that of SPM, and the magnitude of instability is generally larger than that of each mode alone. The implications for parametric process and wavelength exchange in optical physics with two pump waves are discussed.     

托卡马克中漂移不稳定性的回旋动理学二维本征模方程

从弗拉索夫方程出发,导出了托卡马克等离子体中漂移不稳定性的回旋动理学二维本征模积分方程组。该方程组保留了离子的动理学效应,包括沿磁场的运动、磁场梯度和曲率漂移以及有限拉莫半径效应。与传统的采用气球模表象得到的一维回旋动理学方程(其只能给出不稳定模沿磁场线的结构)不同,该方程组不仅能给出托卡马克等离子体中漂移不稳定模的径向结构,同时还考虑了由离子的环形性漂移引起的相邻极向模之间的线性耦合,进而得到模的极向结构。该结果为相应的数值模拟研究提供了理论基础。     

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…     

High-speed modal decomposition of mode instabilities in high-power fiber lasers

A high-speed mode analysis technique is required to gain fundamental understanding of mode instabilities in high-power fiber laser systems. In this work a technique, purely based on the intensity profile of the beam, is demonstrated to be ideally suited to analyze fiber laser dynamics. This technique, together with a high-speed camera, has been applied to the study of the temporal dynamics of mode instabilities at high average powers with up to 20,000 frames per second. These measurements confirm that energy transfer between the fluctuating transversal modes takes place in millisecond-time-scale.     

High-purity transmission of a slow light odd mode in a photonic crystal waveguide

We demonstrate a novel scheme to control the excitation symmetry for an odd mode in a photonic crystal waveguide and investigate the spectral signature of this slow light mode. An odd-mode Mach-Zehnder coupler is introduced to transform mode symmetry and excite a high-purity odd mode with 20?dB signal contrast over the background. Assisted by a mixed-mode Mach-Zehnder coupler, slow light mode beating can be observed and is utilized to determine the group index of this odd mode. With slow light enhancement, this odd mode can help enable novel miniaturized devices such as one-way waveguides.