Wave Resonance in Media with Modular,Quadratic and Quadratically-Cubic Nonlinearities Described by Inhomogeneous Burgers-Type Equations

The phenomenon of “wave resonance” which occurs at excitation of traveling waves in dissipative media possessing modular, quadratic and quadratically-cubic nonlinearities is studied. The mathematical model of this phenomenon is the inhomogeneous (or “forced”) equation of Burgers type. Such nonlinearities are of interest because the corresponding equations admit exact linearization and describe real physical objects. The presence of “accompanying sources” (traveling with the wave) on the right-hand side of the inhomogeneous equations ensures the inflow of energy into the wave, which thereafter spreads throughout the wave profile, flows to emerging shock fronts, and then dissipates due to linear and nonlinear losses. As an introduction, the phenomenon of wave resonance in ideal and dissipative media is described and physical examples are given. Exact expressions for nonlinear steady-state wave profiles are derived. Non-stationary processes of wave generation, spatial “beating” of amplitudes with different relationship between the speed of motion of the sources and the natural wave velocity in the medium are studied. Resonance curves are constructed that contain a nonlinear shift of the absolute maxima to the “supersonic” region. The features of the resonance in each of the three types of nonlinearity are discussed.     

Formation and Classification of Jumps and Solitary Shock Waves in Isentropic Flows of Polytropic Continuous Media

JETP Letters - Conditions for an arbitrary jump occurrence in isentropic flow are studied. It is shown that the jump in gas-dynamic parameters arises as a result of the evolution of a self-similar...     

Alfvén Waves in Non-Stationary and Non-Uniform Media: An Exactly Solvable Model

The modulation of Alfvén waves interacting with a non-uniform and non-stationary plasma is considered. The waveforms are allowed to change rapidly. We examine our phenomena by means of exact analytical solutions of the MHD equations in the presence of large amplitude disturbances of the magnetic field and plasma density. In contrast to the WKB approach, we do not have to use limiting assumptions regarding the variations of the background medium. We show that the large amplitude time and space disturbances lead to a new cut-off frequency for Alfvén wave propagation. A rapid reshaping of the Alfvén waveform can also obstruct the resonant interactions between the waves and the plasma particles.     

广义特征坐标系计算膨胀波与激波优越性的数值验证

最近提出的以流体速度和声速的线性组合为速度而运动的广义特征坐标系,是-个更为-般的坐标系统,当参数取不同特殊值的时候,就可以得到其他经典的坐标系统.这种坐标系的最大特点是,它能跟随膨胀波(当然也可以跟随激波和接触间断)运动,从而在使用同-计算格式的前提下,使得膨胀波的计算精度更高.对膨胀波和激波进行数值试验,结果显示广义特征坐标系在计算膨胀波和激波时明显优于传统的坐标系.     

An Alternative Approach to Obtain the Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p+p(1/x) Terms

By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics 42, 853]. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

Propagation of Electron Acoustic Soliton,Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic(EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated.A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation.Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions.The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically.In the presence of the Burgers term,the EXP-function method is used to solve the Kadomstev-Petviashvih-Burgers equation and the obtained solution is related to shock wave.The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.     

Propagation of Electron Acoustic Soliton,Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev-Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.     

天体物理、引力波及重离子碰撞中的物质

通过相对论性磁流体力学的计算知道,由双中子星合并产生的引力波对中子星内部是否存在夸克物质以及QCD物质状态方程的硬度度非常敏感。这些天文学上创造的热力学极限在20%以内跟某些快度、碰撞参数等条件下的相对论重离子碰撞产生的温度和密度相当。本文结合相对论模拟双中子星系统及实验室中重离子碰撞的结果,从而确定高密物质的状态方程和相结构。讨论了中子星合并后残留物的引力波发射,这将有助于了解夸克强子过渡的性质。     

White-Noise and Geometrical OpticsLimits of Wigner–Moyal Equation for Beam Waves in Turbulent Media II: Two-Frequency Formulation

We introduce two-frequency Wigner distribution in the setting of parabolic approximation to study the scaling limits of the wave propagation in a turbulent medium at two different frequencies. We show that the two-frequency Wigner distribution satisfies a closed-form equation (the two-frequency Wigner–Moyal equation). In the white-noise limit we show the convergence of weak solutions of the two-frequency Wigner–Moyal equation to a Markovian model and thus prove rigorously the Markovian approximation with power-spectral densities widely used in the physics literature. We also prove the convergence of the simultaneous geometrical optics limit whose mean field equation has a simple, universal form and is exactly solvable     

Dispersion Laws,Nonlinear Solitary Waves,and Modeling of Kernels of Integro-Differential Equations Describing Perturbations in Hydrodynamic-Type Media With Strong Spatial Dispersion

Acoustical Physics - An integro-differential equation simulating a medium with strong spatial dispersion and hydrodynamic-type nonlinearities (the Whitham equation) is considered. A method is...