大尺度浅水波方程中相互调制的非线性波

基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象. 关键词： 浅水波方程 大尺度正压大气 解析解 非线性波     

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.     

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.     

Rogue Waves in the (2+1)-Dimensional Nonlinear Schrodinger Equation with a Parity-Time-Symmetric Potential

The(2+1)-dimension nonlocal nonlinear Schrodinger(NLS) equation with the self-induced parity-time symmetric potential is introduced, which provides spatially two-dimensional analogues of the nonlocal NLS equation introduced by Ablowitz et al. [Phys. Rev. Lett. 110(2013) 064105]. General periodic solutions are derived by the bilinear method. These periodic solutions behave as growing and decaying periodic line waves arising from the constant background and decaying back to the constant background again. By taking long wave limits of the obtained periodic solutions, rogue waves are obtained. It is also shown that these line rogue waves arise from the constant background with a line profile and disappear into the constant background again in the(x,y) plane.     

Bifurcation methods of dynamical systems for generalized Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation

By applying the bifurcation theory of dynamical system to the generalized KP-BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are obtained.      

Quasi-Periodic Solutions and Asymptotic Properties for the Isospectral BKP Equation

In this paper, based on a Riemann theta function and Hirota's bilinear form, a straightforward way is presented to explicitly construct Riemann theta functions periodic waves solutions of the isospectral BKP equation. Once the bilinear form of an equation obtained, its periodic wave solutions can be directly obtained by means of an unified theta function formula and the way of obtaining the bilinear form is given in this paper. Based on this, the Riemann theta function periodic wave solutions and soliton solutions are presented. The relations between the periodic wave solutions and soliton solutions are strictly established and asymptotic behaviors of the Riemann theta function periodic waves are analyzed by a limiting procedure. The N-soliton solutions of isospectral BKP equation are presented with its detailed proof.     

Quasi-Periodic Solutions and Asymptotic Properties for the Isospectral BKP Equation

In this paper, based on a Riemann theta function and Hirota's bilinear form, a straightforward way is presented to explicitly construct Riemann theta functions periodic waves solutions of the isospectral BKP equation.Once the bilinear form of an equation obtained, its periodic wave solutions can be directly obtained by means of an unified theta function formula and the way of obtaining the bilinear form is given in this paper. Based on this, the Riemann theta function periodic wave solutions and soliton solutions are presented. The relations between the periodic wave solutions and soliton solutions are strictly established and asymptotic behaviors of the Riemann theta function periodic waves are analyzed by a limiting procedure. The N-soliton solutions of isospectral BKP equation are presented with its detailed proof.     

Nonlinear theory of ion-sound waves in a dusty electron-positron-ion plasma

A theory of ion-sound waves in a dusty electron-positron-ion plasma is developed. It is shown in the linear approximation that periodic waves exist in a bounded range of parameters. The expression for the sound velocity is derived and the dependence of the velocity on the space charge of dust particles is analyzed. In the nonlinear theory, the general exact solution is obtained, which is then analyzed using the Bernoulli pseudopotential method. Particular solutions are obtained in the form of nonlinear periodic waves, large-amplitude periodic waves (superlinear waves), and solitary compression and rarefaction waves (solitons).     

Periodic Folded Wave Patterns for (2+1)-Dimensional Higher-Order Broer-Kaup Equation

A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-order Broer-Kaup equation by means of WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are found to be completely elastic.     

Study on Solitary Waves of a General Boussinesq Model

In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the travelling wave systems are obtained. The possible solitary wave solutions, periodic wave solutions and cusp waves for the general Boussinesq type fluid model are also investigated.     

Production of materials with periodically arranged microparticles by photopolymerization of patterns formed at parametric excitation of capillary surface waves

It is experimentally demonstrated that parametric excitation of capillary waves in a liquid polymer can result in a spatially periodic distribution of microparticles. The distribution of the particles follows the pattern of the waves excited on the surface of the liquid. It is shown that photopolymerization allows positions of microparticles to be fixed and materials with controlled spatially periodic inhomogeneity to be produced.     

Bragg Interaction of Surface Magnetostatic Waves with a Periodic Granular High-Temperature Superconducting Structure

Bragg interaction of surface magnetostatic waves with a periodic granular high-temperature superconducting structure is studied. A dispersion equation for coupled waves describing the characteristics of surface magnetostatic waves is derived. Resonance wave absorption near the critical temperature is revealed. The magnetostatic wave reflection coefficients of semi-infinite and finite periodic high-temperature superconducting structures are calculated. The results obtained can be used in designing tunable frequency selectors and transient bolometric photodetectors.     

Periodic folded waves for a （2＋1）-dimensional modified dispersive water wave equation

A general solution, including three arbitrary functions, is obtained for a (2+1)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.     

Spontaneous emission from Bloch states of a two-level atom in a periodic field of the biparabolic shape

By analogy with the Wigner-Weisskopf model, spontaneous emission of an atom is considered in a spatially periodic field of the resonance counter-propagating waves. The Bloch state obtained by the interaction of the initially excited (unexcited) atom with a field of the counter-propagating waves plays the role of the excited (ground) state of the free atom. The spontaneous emission probability averaged over polarizations is shown to become anisotropic, with the symmetry axis directed along the wave propagation path. The anisotropy is caused by the spatially periodic distribution of the wave function of the translational motion of an atom in the external field. The degree of anisotropy depends on the position of Bloch energy levels in the allowed bands of the energy spectrum.     

Periodic current domains in a system of carbon nanotubes

The dynamics of propagation of periodic electromagnetic waves and the current induced by them in a system of carbon nanotubes is investigated. The study is performed on the basis of the analysis of the coupled equations for the classical distribution function of electrons in carbon nanotubes and the Maxwell equations for an electromagnetic field. An effective equation describing the electromagnetic field dynamics is obtained. Periodic changes in the form of an electromagnetic wave during its propagation are revealed. This effect is related to the energy exchange between periodic vibrations with different periods in the system under consideration. The corresponding regions of the current through carbon nanotubes form a regular periodic domain structure. The results of numerical calculations are reported, which make it possible to consider this effect at different problem parameters.     

Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity by mapping and ansatz methods

Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity are obtained using the mapping method. Several solutions are determined inclusing the cnoidal waves, shock waves, solitary waves, periodic singular waves and others. Finally, the ansatz method is applied to solve the equation with power law nonlinearity. It has been proved that the shock waves or topological solitons exist only for specific values of the power law parameter.     

Bifurcation analysis of nonlinear and supernonlinear dust–acoustic waves in a dusty plasma using the generalized (r,q) distribution function for ions and electrons

Bifurcation analysis of dust acoustic (DA) periodic waves in three components, unmagnetized dusty plasma system is investigated using the generalized (r, q) distribution function for ions and electrons. Depending on the different parameters of the system considered, all possible phase portraits, including periodic, homoclinic, superperiodic, and superhomoclinic trajectories, are presented. The existence of rarefactive and compressive solitary waves is proved. Also, the plasma system under consideration supports both nonlinear and supernonlinear DA periodic waves. It has been found that the double spectral indices r and q play a decisive effect on the bifurcation of the waves.     

Transient dynamics of charged particles interacting with localized waves of continuous spectra

A modified canonical perturbation method is employed for analyzing the charged particle dynamics as they interact with localized waves with continuous spectrum. In contrast with periodic Hamiltonian models, where the method has already been applied in a multitude of respective systems, the system in hand is inherently aperiodic. The localized waves have the form of amplitude modulated electrostatic fields, ranging from ordinary wave packets to ultrashort pulses. The analytically obtained approximate invariants of the motion contain rich information for the structure of the phase space and the respective distribution functions.     

Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV--mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.     

基于叠栅技术的二维亚波长周期结构成像设计

用光子学方法研究了叠栅技术中,当试件光栅被拉压和旋转后,叠栅条纹的空间周期和相对于基准光栅的取向,试件光栅被拉压后的节距等相关问题。根据衍射光波的空间周期可能大于试件光栅空间周期的特点,对二维亚波长周期结构衍射成像进行了设计研究。首先,对二维亚波长周期结构衍射物进行编码,以获得包含编码光栅空间信息的均匀波;其次,使编码得到的均匀波通过光学系统,并被放大到CCD相机所能辨识的大小;再次,经解码光栅解码,滤掉编码波,最终获得二维亚波长周期结构物的空间结构信息,达到超分辨的目的。同时,对成像过程进行了较为详尽的分析,对编码器、解码器的位置以及它们相对衍射物的取向进行了设计研究,对滤波器的选择给予了必要的说明,指出了取得超分辨成像的关键。