Transformation of a nonlinear plasma wave into electromagnetic radiation in a periodic magnetic field

We study transformation of a nonlinear plasma wave into electromagnetic radiation in the periodic static magnetic field of an undulator. Such a wave can be excited by a short laser pulse or a relativistic electron bunch. The features of relativistic upper-hybrid plasma oscillations are analyzed. In the approximation of constant pump, resonance conditions of excitation of an electromagnetic wave and the characteristic transformation length are found. The nonlinear stage of transformation with allowance for pump depletion is considered. The studied phenomenon can be used for development of a high-power terahertz-radiatoin source. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 496–507, June 2007.     

Spatial four wave mixing in nonlinear periodic structures

We present the first experimental study of spatial four-wave mixing in photonic lattices, demonstrating universal aspects of nonlinear processes in periodic media, such as engineered phase matching, Bloch-wave folding, and continuous control over the band at which the interaction products emerge.     

The periodic wave solutions for two systems of nonlinear wave equations

The periodic wave solutions for the Zakharov system of nonlinear wave equations and a long－short-wave interaction system are obtained by using the F-expansion method, which can be regarded as an overall generalization of Jacobi elliptic function expansion proposed recently. In the limit cases, the solitary wave solutions for the systems are also obtained.     

Unveiling quasiperiodicity through nonlinear wave mixing in periodic media

Quasiperiodicity is the concept of order without translation symmetry. The discovery of quasiperiodic order in natural materials transformed the way scientists examine and define ordered structure. We show and verify experimentally that quasiperiodicity can be observed by scattering processes from a periodic structure, provided the interaction area is of finite width. This is made through a momentum conservation condition, physically realizing a geometrical method used to model quasiperiodic structures by projecting a periodic structure of a higher dimension.     

Resonant interaction of the Langmuir wave with quasi-stationary plasma electrons

Evolution of the Langmuir wave in quasi-stationary plasma is considered. A consistent solution to the closed system of the Vlasov–Poisson equations is obtained in the adiabatic approximation. Dispersion of the wave evolving in the electron distribution tail with variable electron concentration or plasma temperature is described. It is established that the plasma oscillation energy increases with decreasing electron concentration or increasing temperature. After plasma regains its initial state, the wave parameters also restore their initial values. That is, the wave evolution in the quasi-stationary plasma is a completely reversible process.     

Diffraction reflection of light on natural periodic inhomogeneities of a crystal with open surface of wave vectors

The forms of the surface of wave vectors for an extraordinary wave in the presence and absence of absorption are discussed. The normal transmission of light through a plane-parallel layer of a crystal with an open surface of wave vectors is considered. The diffraction reflection of light on natural periodic inhomogeneities of a crystal is studied. The frequency dependence of the reflection coefficient is calculated.     

Quantized vortex stability and interaction in the nonlinear wave equation

The stability and interaction of quantized vortices in the nonlinear wave equation (NLWE) are investigated both numerically and analytically. A review of the reduced dynamic law governing the motion of vortex centers in the NLWE is provided. The second order nonlinear ordinary differential equations for the reduced dynamic law are solved analytically for some special initial data. Using 2D polar coordinates, the transversely highly oscillating far field conditions can be efficiently resolved in the phase space, thus giving rise to an efficient and accurate numerical method for the NLWE with non-zero far field conditions. By applying this numerical method to the NLWE, we study the stability of quantized vortices and find numerically that the quantized vortices with winding number m=±1 are dynamically stable, and resp. |m|>1 are dynamically unstable, in the dynamics of NLWE. We then compare numerically quantized vortex interaction patterns of the NLWE with those from the reduced dynamic law qualitatively and quantitatively. Some conclusive findings are obtained, and discussions on numerical and theoretical results are made to provide further understanding of vortex stability and interactions in the NLWE. Finally, the vortex motion under an inhomogeneous potential in the NLWE is also studied.     

非线性波动方程的Jacobi椭圆函数包络周期解

应用Jacobi椭圆函数展开法求得了一类非线性波方程的包络周期解,而且用这种方法得到的周期解在一定条件下可以退化为包络冲击波解或包络孤立波解 关键词： Jacobi椭圆函数 非线性方程 包络周期解 包络孤立波解     

一类非线性方程的新周期解

把Jacobi椭圆函数展开法扩展到Jacobi椭圆余弦函数和第三类Jacobi椭圆函数的有限展开法,并给出了一类非线性波动方程的新周期解,并且应用这种方法得到的周期解也可以退化为冲击波解或孤波解. 关键词： Jacobi椭圆函数 非线性方程 周期解 孤波解     

圆杆波导中的一个非线性波动方程及准确周期解

在小变形条件下，采用Cox的非线性应力应变关系，计及横向Possion效应，借助Hamilton变分原理导出了非线性弹性圆杆波导中的纵向波动方程. 利用Jacobi椭圆余弦函数展开法，对该方程与截断的非线性波动方程进行求解，得到了两类非线性波动方程的准确周期解，它们可以进一步退化为孤波解. 关键词： 非线性波 Possion效应 Jacobi椭圆余弦函数