Elastic Wave Velocities in Two-component Systems

The problem is formulated for the scattering of long wavelengthplane elastic waves by a single homogeneous obstacle in an infiniteelastic medium. The problem differs from earlier studies inthat discrete differences in the physical properties are permittedto exist at the boundary. Earlier treatments of the scatteringproblem in which the Green's function for the scatterer is asimple operation on the incident field are inadequate to accountfor the refraction of the field at the boundary. For the caseof scattering of long waves by a spherical obstacle the scatteredfields are shown to involve the elastic constants in identicallythe same way as does the static field for the same geometryin the presence of a uniform static field. As a special casea new solution is given for the static problem of the inhomogeneousinclusion. A wave equation is derived for the "average" fielddue to multiple scattering by a statistical distribution ofspheres. The macroscopic wave parameters for the long wavelengthapproximation are obtained as a weighted contribution of theproperties of the two components.     

Nonlinear Wave Interactions in Nonlinear Nonintegrable Systems

The main goal of this article is to understand the qualitative appearances of regular arrays of pulses that come up in nonintegrable systems in a variety of contexts, particularly in fluid dynamics. It is shown that even nonintegrable systems have a kind of particle dynamics made up of solitary waves. But the interaction of these solitary waves is not absolutely “clean” as in the case of the KdV and other integrable equations.     

修正迭代法在波纹圆板非线性振动问题中的应用

在本文中,我们将修正迭代法成功地推广运用于全波纹圆板的非线性振动问题的研究,获得了全波纹圆板的非线性振频和振幅的解析关系式.本文还讨论了波纹圆板的几何参量对其振动特性的影响,本文结果对精密仪器弹性元件的设计具有一定的实际意义.     

非线性弹性杆波动方程的显式精确解北大核心CSCD

应用sine-cosine方法对非线性弹性杆波动方程进行了求解,得到了该方程的一些新的周期波解和孤波解(材料常数n为不等于1的常数).对部分结果通过数学软件得到了解的图像,获得的结果有助于非线性弹性杆中孤波存在性问题的进一步研究.     

修正迭代法在薄圆板非线性后屈曲分析中的应用

本文进一步将修正迭代法推广到薄圆板轴对称后屈曲分析中,由此获得该问题的一种新的近似解析解.作者期望将此方法应用于更为复杂结构的板的后屈曲分析中去.     

Group Classifications, Symmetry Reductions and Exact Solutions to the Nonlinear Elastic Rod Equations

In this paper, the Lie symmetry analysis are performed on the three nonlinear elastic rod (NER) equations. The complete group classifications of the generalized nonlinear elastic rod equations are obtained. The symmetry reductions and exact solutions to the equations are presented. Furthermore, by means of dynamical system and power series methods, the exact explicit solutions to the equations are investigated. It is shown that the combination of Lie symmetry analysis and dynamical system method is a feasible approach to deal with symmetry reductions and exact solutions to nonlinear PDEs.     

Some Properties of Nonlinear Wave Systems

The results of a preliminary study of a particular nonlinear system of partial differential equations are presented. While much of this work pertains to two coupled nonlinear Schrödinger equations, it is believed that the properties found are representative of many other dispersive wave systems.     

非线性弹性地基上的圆薄板的分岔与混沌问题

根据非线性弹性地基上圆薄板大幅度方程,弹性抗力有线性项,三次非线性项和抗弯曲弹性项。在周边固定的条件下,利用Galerkin法得到了一个非线性振动方程。在无外激励情况下,求出在平衡点处的Floquet指数。分析了其稳定性与可能发生的分岔条件。在外激励条件下,用Melnikov方法分析研究了可能发生的混沌振动。通过数字仿真给出了各种地基参数下混沌区域的临界曲线和相平面图。     

渐近法在一类强非线性系统中的应用

本文采用文[1、2]的渐近解形式,将渐近法推广到如下较为广泛一类的强非线性振动系统式中g和f为x,的非线性解析函数,ε>0为小参数,并假设对应于ε=0的派生系统有周期解.本文推得系统(0.1)的渐近解递推方法,并应用于实例.     

Convergence of Empirical Processes for Interacting Particle Systems with Applications to Nonlinear Filtering

In this paper, we investigate the convergence of empirical processes for a class of interacting particle numerical schemes arising in biology, genetic algorithms and advanced signal processing. The Glivenko–Cantelli and Donsker theorems presented in this work extend the corresponding statements in the classical theory and apply to a class of genetic type particle numerical schemes of the nonlinear filtering equation.     

Justification of Averaging Method for Multifrequency Impulsive Systems

We prove new theorems on the justification of the averaging method for multifrequency oscillation systems with pulse influence at fixed times.     

一类非线性波动方程的势对称分类

先给出了含有一个任意函数的线性波动方程的古典和势对称的完全分类.然后,在此基础上给出了含有两个任意函数的一类非线性波动方程的两种情形势对称分类,得到了该方程的新势对称.在处理对称群分类问题的难点-求解确定方程组时我们提出了微分形式吴方法算法,克服了以往难于处理的困难.在整个计算过程中反复使用了吴方法,吴方法起到了关键的作用.     

一类非线性弹性杆波动方程的求解

对计入横向惯性效应后的非线性弹性杆纵向波动方程进行了分析,得到了一类非线性波动方程,并用完全近似方法求出了该方程的近似解析解．     

Nonresonance and Global Existence of Nonlinear Elastic Wave Equations with External Forces

This paper establishes the global existence of classical solution to the system of homogeneous,isotropic hyperelasticity with time-independent external force,provided that the nonlinear term obeys a ty...     

Perturbative Analysis of Wave Interaction in Nonlinear Systems

We propose a new way to handle obstacles to asymptotic integrability in perturbed nonlinear PDEs in the method of normal forms (NFs) in the case of multiwave solutions. Instead of including the whole obstacle in the NF, we include only its resonant part (if it exists) in the NF and assign the remainder to the homological equation. This leaves the NF integrable, and its solutions retain the character of the solutions of the unperturbed equation. We use the freedom in the expansion to construct canonical obstacles that are confined to the interaction region of the waves. For soliton solutions (e. g., of the KdV equation), the interaction region is a finite domain around the origin; the canonical obstacles then do not generate secular terms in the homological equation. When the interaction region is infinite (or semi-infinite, e.g., in wave-front solutions of the Burgers equation), the obstacles may contain resonant terms. The obstacles generate waves of a new type that cannot be written as functionals of the solutions of the NF. When the obstacle contributes a resonant term to the NF, this leads to a nonstandard update of the wave velocity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 410–422, August, 2005.     

Averaging of Systems with Slow Variables

We justify the averaging method for systems with delay described by both slow and fast variables. The results obtained are applied to the analysis of one problem in control theory.     

Error Estimates for the Averaging Method for Pulse Oscillation Systems

We prove new theorems on the justification of the averaging method on a segment and semiaxis in multifrequency oscillation systems with pulse action at fixed times.     

非线性弹性杆波动方程的摄动分析

针对计入横向惯性效应后的非线性弹性杆纵向波动方程进行了分析．在小振幅、长波长的一般情况下,根据远方场简单波理论,采用约化摄动法,得到了NLS方程,并讨论了存在NLS孤子的条件．