Nonsteady waves in distributed dynamical systems

The paper is devoted to the study of one-dimensional and two-dimensional transient wave regimes in nonlinear systems of the reaction-diffusion type. In a one-dimensional case the process of collision of two travelling waves is considered. It is demonstrated that in the case of a nondispersive nonlinear system, where a steady regime of the collision is not possible, the process can be described by means of an approximation which is nonuniform in a spatial coordinate. The collision results, in a general case, in formation of an oscillatory shock wave moving with varying velocity. In a two-dimensional situation the transition of a rotating vortex into a rotating spiral wave in the case of dispersive systems and the inverse transition in the case of nondispersive systems are considered.     

Three-wave interaction in a self-gravitating fluid

Nonlinear three-wave interaction is investigated in rotating self-gravitating astrophysical fluids. Both direct and inverse cascades are found. The latter should be of importance for the formation of structures in rotating astrophysical objects like protogalaxies and galaxies. Linear gravitational instability is shown to be a process that develops on much longer time scales, compared to the nonlinear wave interaction, and the nonlinear precipitation of energy from the linearly unstable, slowly contracting mode towards smaller spatial and time scales is shown to be possible.     

Nonlinear modes in rotating double well potential with parity–time symmetry

We investigate the nonlinear modes in a rotating double well potential with 79T symmetry. Focus on the existence and stability of the nonlinear PT modes in this system, we found that five types of PT modes can stably exist by given certain parameter settings. The multistable area between these modes are studied numerically and the bistable and tristable areas are delimited. With different input trial wavefunctions, five types of solitary wave modes are identified. We found that the rotating of the potential can significantly affect the power flow of the fundamental harmonic mode, whose effect is absent for the other modes.     

有偏压的光伏光折变晶体中屏蔽光伏孤子的自偏转

修正了有偏压的光伏光折变晶体中屏蔽光伏孤子的理论。用微扰法研究了屏蔽光伏孤子的自偏转，得出孤子光呸中心的运动为抛物线，并且空间频率分量随传播距离而线性移动，改变外偏压或旋转光的偏振方向可以控制其自偏转。当光伏效应可忽略时，屏蔽光伏孤子的非线性波动方程就转化为屏蔽孤子的非线性波动方程，它的自偏转就转化为屏蔽孤子的自偏转。当外偏压为零时，屏蔽光伏孤子的非线性波动方程就转化为光伏孤子的非线性波动方程，它的自偏转证明了光伏孤子中也存在着自偏转。     

Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings

We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.     

Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings

We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.     

Nonlinear interaction between a two-level atom and a weak polychromatic field

The interaction between two-level media and a polychromatic field is considered in the limit of small field amplitudes. The obtained third-order corrections allow us to describe a nonlinear response to the field and intermodal interaction. The obtained polarization spectra are compared to numerical solutions to the density matrix equation in the rotating wave approximation. The results can be used in nonlinear comb spectroscopy.     

Fluid echoes in a pure electron plasma

Experimental observations of diocotron wave echoes on a magnetized electron column are reported, representing Kelvin wave echoes on a rotating near-ideal fluid. The echoes occur by reversal of an inviscid wave damping process, and the phase-space mixing and unmixing are directly imaged. The basic echo characteristics agree with a simple nonlinear ballistic theory. At late times, the echo is degraded, and the maximal observed echo times agree with a theory of electron-electron collisions acting on separately evolving velocity classes.     

离子晶格非简谐振动引起的光学非线性与增强吸收型光双稳

处理了光场（电磁场）与离子晶体的非简谐性振动之间的相互作用问题。导出了用简正坐标即声子模式所表达的非线性晶格动力学和非线性宏观极化。在旋转波近似下，得到在入射光驱动下光子－声子耦合体系的总的相干性哈密顿算符。通过相应的静态方程证明该耦合系统会出现增强吸收型光学双稳性，这也就证明了光场与各种玻色子型固体元激发，如光频支声子和半导体中激子的非线性耦合可以作为增强吸收型光双稳的机制。     

Characterizing continuously rotating detonation via nonlinear time series analysis

The sampled pressure signals in continuously rotating detonation combustors have the inherence of nonlinear dynamics. To dig out more information on combustion modes, the nonlinear time series analysis method is thus applied to the pressure-time series obtained at a hydrogen/air rotating detonation combustor by using the phase space reconstruction and wavelet entropy algorithm. The variation of wavelet entropy is approved to be associated with the periodicity variation of pressure signals. Different structures of attractor as well as wavelet entropy distribution in the phase diagram can distinguish the deflagration mode from the unstable and stable detonation modes under the conditions of different air flow rates. The limit-cycle oscillation is exhibited in the phase space diagram with a very low flow rate, here 25 g/s. The mean wavelet entropy of pressure-time series can be a quantitative index of different combustion modes occurring in the combustor. The present study is expected to enhance the understanding of the physical mechanism of continuously rotating detonation and contribute on the development of detonation propulsion technology.     

Strain wave evolution equation for nonlinear propagation in materials with mesoscopic mechanical elements

Nonlinear wave propagation in materials, where distribution function of mesoscopic mechanical elements has very different scales of variation along and normally to diagonal of Preisach-Mayergoyz space, is analyzed. An evolution equation for strain wave, which takes into account localization of element distribution near the diagonal and its slow variation along the diagonal, is proposed. The evolution equation provides opportunity to model propagation of elastic waves with strain amplitudes comparable to and even higher than characteristic scale of element localization near Preisach-Mayergoyz space diagonal. Analytical solutions of evolution equation predict nonmonotonous dependence of wave absorption on its amplitude in a particular regime. The regime of self-induced absorption for small-amplitude nonlinear waves is followed by the regime of self-induced transparency for high-amplitude waves. The developed theory might be useful in seismology, in high-pressure nonlinear acoustics, and in nonlinear acoustic diagnostics of damaged and fatigued materials.     

一维Klein-Gordon/Fermi-Pasta-Ulam混合原子链中非线性参数作用的研究

采用推广的旋转平面波近似对一维非线性Klein-Gordon/Fermi-Pasta-Ulam混合原子链的运动方程进行简化,数值求解得到该系统中存在的离散呼吸子解.研究了系统中各非线性参数对该振动模的直流、一阶简谐项和二阶简谐项三个分量的对称性的影响以及对系统中局域模的影响. 关键词： Klein-Gordon/Fermi-Pasta-Ulam混合原子链 推广的旋转平面波近似 离散呼吸子 对称性     

Plasma wave frequency shift in a weak transverse magnetic field due to trapped particle acceleration

A simple model of nonlinear electrostatic wave–particle interaction in a weak magnetic field perpendicular to the direction of wave propagation is developed. The damping of the wave loaded with the phase bunched groups of trapped particles is considered with the aid of the model equations. To determine the nonlinear frequency shift of the wave in the process of the trapped particle acceleration, the nonlinear dispersion equation is derived. It is shown that the corresponding variation of the phase velocity may affect the interaction process and hence must be taken into account in the self-consistent treatment of the time evolution of the wave.     

Ion velocity distribution function investigated inside an unstable magnetized plasma exhibiting a rotating nonlinear structure

The frequent situation where a strongly nonlinear rotating structure develops in a linear magnetized plasma column is investigated experimentally with emphasis on the ion velocity distribution function (IVDF). Most often, a mode m=2 appears exhibiting a large density and potential perturbation with angular frequency slightly above the ion cyclotron frequency. For the first time the spatiotemporal evolution of the IVDF is studied using time-resolved laser induced fluorescence to explore the ion's interaction with the nonlinear wave propagating inside the column and at the origin of plasma transport outside the limiter. The ion fluid exhibits an alternance from azimuthal to radial velocity due to the electric field inside the rotating structure. A fluid model also allows us to locally reconstruct the self-consistent electric field evolution which contradicts all existing theories.     

Reflection and transmission of circularly polarized waves in nonlinear dielectrics

A time-sinusoidal circularly polarized plane standing wave solution is obtained for isotropic lossless dielectric media with arbitrary nonlinearity. The spatial variation of the standing wave depends on the nonlinearity and is found by solving a problem of centralforce motion in which the electric complementary energy density furnishes the potential and the spatial coordinate has the role of time. Two special nonlinear dielectric response laws-cubic and quintic-are treated, and explicit solutions for the spatial variation of the wave amplitude and phase are obtained in terms of elliptic functions and elliptic integrals, respectively. The standing-wave solution is applied to give steady state solutions of two reflection/transmission problems (a) reflection from, or resonance modes between, ideally conducting planes and (b) reflection and transmission at a plane interface between two nonlinear dielectric media.     

Coupled Soliton States and Localization of Cnoidal Waves at the Interface of Nonlinear and Linear Media

Contact effects at the interface of linear and nonlinear media are studied. The problem of different stationary states in two-level system with different parameters of the dispersion relation is considered. A model that employs the nonlinear Shrödinger equation is used to show coupled states of solitons, localization of waves on one side of a defect, and transformation of nonlinear wave into linear wave upon transition through interface for the system under study due to variation in energy. Dispersion relations that determine the energies of such states are derived.     

Ultrasonic waves in crystals with charged dislocations

A system of equations for charged dislocations, where the quadratic nonlinear terms are taken into account, is derived using the variational principle. This system describes the propagation of ultrasonic (US) waves in crystals with charged dislocations. From the linearized system of equations a linear dispersion equation is derived. Formulas for the phase linear velocity of the wave and the absorption coefficient are obtained, which show essential influence of charged dislocations and electrical properties of media on the mentioned quantities. For a nonlinear US wave an equation for the amplitude of the first harmonic is derived and, as a consequence, expressions are obtained for the nonlinear velocity of the US wave, for the attenuation of the first harmonic's amplitude, and for phase variation.     

Riddling of the orbit in a high dimensional torus and intermittent energy bursts in a nonlinear wave system

The bifurcation scenario in a practically interesting nonlinear wave system is investigated by using a new scheme that is performed in a purely nonlinear wave framework with the Doppler effect taken into account. High-dimensional tori with three or four competing frequencies are observed. With variation of parameters a riddling of the orbit may occur intermittently due to tangency in certain dimensions, which temporarily spoils the toroidal topology and induces an energy burst where spatial coherence of the wave is lost.     

Wave pattern motion and stick-slip limit cycle oscillation of a disc brake

This paper examines the dynamic response of a rotating squealing disc brake subject to distributed nonlinear contact stresses where two brake pads are assumed to be stationary and rigid. The friction stresses produce high-frequency vibrations that exhibit standing or traveling waves on the disc surface. The wave pattern resulting from the binary flutter mechanism of one transverse doublet mode pair is studied here. The results show that the wave pattern is associated with mode-coupling character. For a steady-squealing mode, the stick zone of the contact area is determined by a smooth friction-velocity curve having both negative and positive slopes.     

Experimental observation of motion of edge dislocations in Ge/Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>/Si(001) (<Emphasis Type="Italic">x</Emphasis> = 0.2–0.6) heterostructures

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves, two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.