Solitary waves in the Madelung's fluid: Connection between the nonlinear Schrödinger equation and the Korteweg-de Vries equation

An investigation to deepen the connection between the family of nonlinear Schr?dinger equations and the one of Korteweg-de Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis for the current velocity, it is proven that the cubic nonlinear Schr?dinger equation, whose solution is a complex wave function, can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schr?dinger equation, starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u₀ with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined variable x-u_{0 s} (s being a time-like variable). This novel method in solving the nonlinear Schr?dinger equation starting from the Korteweg-de Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the present paper and the ones already known in literature is also presented. Received 20 February 2002 and Received in final form 22 April 2002 Published online 6 June 2002     

声电光效应的耦合波方程理论

将声光效应与电光效应的耦合波方程相结合，统一为声电光效应的耦合波方程，并对之进行求解，给出声电光效应的衍射效率公式。     

在伽利略坐标变换下的二端面弹性转轴相似动力学方程

在非相对论性原理下建立了二端面弹性转轴的相似动力学方程.使弹性转轴的动力学方程与地面坐标下的动力学方程相似,为相似工程学和计量、测控仪器的相似标定提供理论依据及方法 关键词： 二端面弹性转轴 相似模拟 坐标变换 相似动力学方程 标定     

Wave Motions in a Two-Layer Fluid Driven by Small Oscillations of a Cylinder Intersecting the Interface

The plane problem of steady-state small oscillations of a horizontal cylinder located at the interface between two fluids of different densities and indefinite depth is considered in the linear formulation. Boundary integral equations for the surface source distribution are derived. The behavior of the distributed singularities at points of intersection of the body contour and the interface is investigated. The problem of oscillations of a circular cylinder is solved by the multipole expansion method. The apparent mass and damping coefficients of the radiation problem and the reflection coefficient of the problem of scattering of an impinging wave by a floating body are calculated.     

(2+1)维Broer-Kaup-Kupershmidt方程的新精确解

使用变系数的广义Ricatti方程映射法，对（2＋1）维Broer-Kaup—Kupershmidt方程进行了研究，得到了包括Weierstrass函数解、孤立子解、似孤立子解和三角函数解等．由于解的表达式中存在2个或3个任意函数，因此解中存在丰富的结构．     

Evanescent Plane Waves in Multilayer Structures

We have considered evanescent plane waves in structures with a layer of a substance with ε, μ < 0 and with a layer of a well-reflecting metal, ε < 0, μ ≥ 1. Waves with increased amplitude as compared with the initial wave have been found to occur, due to which evanescent waves with wave number as in the initial wave but with increased amplitude arise behind these layers. A composite material with ε, μ < 0 at optical frequencies are proposed. Surface waves on a metal layer are considered in detail. It is shown that surface waves with a sufficiently arbitrary wave number can be excited. It is also shown that, on very thin layers, surface waves with wave number exceeding ten times that of a homogeneous plane wave in vacuum can be excited. Propagation losses are calculated. For a silver layer, the wave path can be from 30 up to 100 wavelengths. Practical use in developing techniques for optical transformations of short-wave surface waves in 2D space, similar to those in 3D space, are pointed out.     

Vertex function and coupling constant for the virtual decay of7Li

The alpha-triton relative wave function with various nucleon exchange contributions and their asymptotic normalization are considered in the framework of the generator coordinate method (GCM). The asymptotic normalization of relative wave function provide the estimate of the coupling constant. The relative wave function is also used to obtain⁷Li-α-t vertex function in the virtual decay of⁷Li. The extrapolation of vertex function for negative values ofq ² up to the alpha-triton pole provide the vertex constant, which is compared with the experimentally determined estimates 0.67 FM and 0.72 FM. Our calculated value is 0.656 FM which is in close agreement with the above estimates.     

冲击波阵面后温度的传导问题

 证明了在一般不计辐射的冲击波阵面后，存在一个热传导波，它的波速完全和冲击波的一致，但阵面后的温度分布有其自己的规律。     

驻波腔内电子运动过程的解析分析

考虑了加速电场的高次谐波的影响，解析地分析了电子在驻波腔内的运动过程，给出了电场分布，与数值模拟计算的电场分布比较吻合。讨论了高次谐波对电子束横向运动的影响，利用此解析解可选择高亮度注入器腔的最优电场分布。并得出射频驻波腔内电子束在β趋于１时射频场效应趋于零的结论。