(1+1)维耦合Ito系统的单值和多值局域激发模式

在(1 1)维非线性动力学系统,人们发现不同的局域激发模式分别存在于不同的非线性系统.可是最近的若干研究表明,在高维非线性动力学系统中,如果选取适当的边值条件或初始条件时,人们可以同时找到若干不同的局域激发模式,如:紧致子、峰孤子、呼吸子和折叠子等.本文的主要目的是寻找(1 1)维非线性耦合Ito系统中的不同的局域激发模式.首先,基于一个特殊的Painlev-éBacklund变换和线性变量分离方法,求得了该系统具有若干任意函数的变量分离严格解.然后,根据得到的变量分离严格解,通过选择严格解中的任意函数,引入恰当的单值分段连续函数和多值局域函数,成功找到了耦合Ito系统若干有实际物理意义的单值和多值局域激发模式,如:峰孤子,紧致子和多圈孤子等.     

Self-Similar Solutions of Variable-Coefficient Cubic-Quintic Nonlinear Schroedinger Equation with an External Potential

An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented.     

Two classes of fractal structures for the （2＋1）-dimensional dispersive long wave equation

Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW) equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.     

New exact excitations and soliton fission and fusion for the （2＋1）-dimensional Broer-Kaup-Kupershmidt system

With the help of an extended mapping approach, a series of new types of exact excitations with two arbitrary functions of the (2 1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific soliton fission and fusion solutions of the higher-dimensional BKK system are also obtained.     

Boussinesq方程的扩展对称约化和新的相似解

将Simon Hood最近提出的扩展Clarkson和Kruskal (CK)方法，推广并应用于Boussinesq方程，得到了该方程的若干新的约化和相似解。该方法也适用于其他有重要物理背景的非线性演化方程。     

(2+1)维Broer-Kaup方程的局域分形结构

进一步拓广齐次平衡法的应用，研究了(2+1)维Broer-Kaup方程的局域分形结构.根据齐次平衡原则，得到方程的B?cklund变换，将方程变换为一个线性化的方程，然后由具有两个 任意函数的种子解构造出一个精确解.利用Jacobian椭圆函数得到了特殊的分形结构. 关键词： 齐次平衡法 (2+1)维Broer-Kaup方程 分形结构     

Exact projective solutions of a generalized nonlinear Schrdinger system with variable parameters

A direct self-similarity mapping approach is successfully applied to a generalized nonlinear Schrdinger (NLS) system. Based on the known exact solutions of a self-similarity mapping equation, a few types of significant localized excitation with novel properties are obtained by selecting appropriate system parameters. The integrable constraint condition for the generalized NLS system derived naturally here is consistent with the known compatibility condition generated via Painlev analysis.     

(3+1)维Burgers系统的新精确解及其特殊孤子结构

将改进的Riccati方程映射法和变量分离法推广到(3+1)维Burgers系统，得到了该系统的新显式精确解.根据得到的孤波解，构造出Burgers系统的几种特殊孤子结构，例如柱状孤子、状孤子和内嵌孤子等，研究了孤子间的相互作用.     

转子扭转-纵向耦合振动分析

针对某转子的模型,分析了扭转-纵向耦合振动.计算结果表明:设置转子预应力与旋转时的离心力相对应,其扭转振动频率将随预应力的增大而增大.转子纵向振动频率不受该预应力的影响,这是因为转子旋转时预应力的方向与轴线垂直.随着转子旋转时预应力的变化,扭转振动频率接近纵向振动频率,出现扭转-纵向耦合振动.     

基于旋转软化的柔性梁动力学研究

建立了旋转柔性梁的非线性动力学模型,利用能量法及哈密顿原理导出了耦合的动力学方程,分析了转动惯性、Coriolis力、应力刚化、旋转软化、加速度、横向位移、弯曲刚度等作用效应;通过设置应力刚化及旋转软化等刚度矩阵和编制有限元程序,建立了梁单元有限元模型,对柔性梁在旋转软化状态下的振动模态进行了数值模拟与分析。计算表明:梁的旋转软化导致其沿旋转平面的弯振模态(摆振)频率随转速增大而相对下降,且对第一阶摆振频率的影响最显著,呈现非线性;梁的旋转软化对垂直于旋转平面的弯振频率几乎没有影响,此结果表明了旋转柔性梁动态特性的复杂性,因此在计算旋转柔性梁的振动特性时,必须同时设置平动、转动惯性质量矩阵,才能获得准确结果。此外,梁单元模型与实体单元模型计算结果误差小于等于5%,验证了本文梁单元模型求解方法的准确性。