色散长波方程的Darboux变换及多孤子解

根据色散长波方程的可积性,首先借助符号计算构造出该方程的Lax对,接着构建一个包含多参数的Darboux变换,通过应用Darboux变换,得到色散长波方程的2N-孤子解,最后通过图像研究了孤子解的性质,这些解和图像可能对解释色散长波方程所描述的水波现象有所帮助.     

(2+1)维色散长波方程新的类孤子解

通过一个简单的变换,将(2+1)维色散长波方程简化为人们熟知的带强迫项Burgers方程,借助Mathematica软件,利用齐次平衡原则和变系数投影Riccati方程法,求出了(2+1)维色散长波方程新的精确解.     

(2+1)维色散长波方程的非局域对称及相容Riccati展开可积性

研究了(2+1)维色散长波方程的非局域对称性和相容Riccati展开(CRE)可积性.首先,通过Painleve分析中的留数对称,将(2+1)维色散长波方程留数对称局域化,得到了与Schwartzian变量相对应的对称群;其次,基于CRE方法,证明了(2+1)维色散长波方程在CRE条件下是可积的;最后,通过求解相容性方程,构造了该方程的孤立波与椭圆周期波的相互作用解.     

(2+1)维色散长波方程的新的相互作用解

根据CRE方法,并结合Jacobi椭圆函数和第三类型不完全椭圆积分,得到了(2+1)维色散长波方程的新的相互作用解,绘制出了每组解在不同时刻的波形图,并阐述了每组解的意义.研究结果充实了(2+1)维色散长波方程的精确解类型.     

色散长波方程簇的Hamilton结构

本文导出了色散长波方程簇,并利用屠规彰迹恒等式方法,讨论它们的Hamil-ton结构。     

分离变量法在变系数(2+1)维方程求解中的应用

分离变量法是求解具有局域相干结构解的有效解析方法.考虑到传播介质的非均匀性和边界的不一致性,变系数(2+1)色散长波方程可以实际地描述宽广的河道或有限深的远海中非线性波的传播.解析研究了变系数(2+1)维色散长波方程.通过分离变量法,得到了该方程组的具有丰富结构的分离变量解.     

一种改善了非线性和色散性的Boussinesq方程模型

推导了一种在不平底上的新的Boussinesq方程．在不增加方程的最高导数项的阶数的情况下提高了模型方程的非线性．为了提高模型的色散性,引入长波近似,通过调节待定系数来使模型的色散性达到Padé(2,2)．对模型方程进行了非线性、线性色散性和线性浅化性分析,分析表明此模型在非线性、色散性和浅化性上都有所提高．将计算结果与实验数据做了比较,结果显示模型更好的符合了实验数据．     

二维色散长波方程组的精确解

利用齐次平衡法给出了二维色散长波方程组的定态解、孤立波解与非孤立波解等几种显式精确解。这个方法也可用来寻找其它非线性发展方程的不同类型的精确解。     

应用拓展的Riccati展开法求非线性发展方程的精确解

借助Mathematica符号计算软件,利用拓展的Riccati展开法和变量分离法,得到非线性发展方程的精确解.通过选择适当的函数,获得(2+1)维色散长波方程的亮暗dromion解.     

(2+1)维色散长波方程的变量分离解

应用改进的G'/G展开法和变量分离法,构造出(2+1)维色散长波方程的变量分离解,根据得到的孤立波解,构造出dromion解,使方程的解变得更加丰富.     

Some new nonlinear wave solutions and their convergence for the (2+1)‐dimensional Broer–Kau–Kupershmidt equation

We use the bifurcation method of dynamical systems to study the (2+1)‐dimensional Broer–Kau–Kupershmidt equation. We obtain some new nonlinear wave solutions, which contain solitary wave solutions, blow‐up wave solutions, periodic smooth wave solutions, periodic blow‐up wave solutions, and kink wave solutions. When the initial value vary, we also show the convergence of certain solutions, such as the solitary wave solutions converge to the kink wave solutions and the periodic blow‐up wave solutions converge to the solitary wave solutions. Copyright © 2014 John Wiley & Sons, Ltd.     

Bifurcation studies on travelling wave solutions for an integrable nonlinear wave equation

By using the method of planar dynamical systems to an integrable nonlinear wave equation, the existence of periodic travelling wave, solitary wave and kink wave solutions is proved in the different parametric conditions. The phase portraits of the travelling wave system are given. It can be shown that the existence of singular curves in the travelling wave system is the reason why the travelling wave solutions lose their smoothness. Moreover, the so-called W/M-shaped solitary wave solutions are obtained.     

Qualitative analysis and explicit traveling wave solutions for the Davey–Stewartson equation

In this paper, we use the bifurcation method of dynamical systems to study the traveling wave solutions for the Davey–Stewartson equation. A number of traveling wave solutions are obtained. Those solutions contain explicit periodic wave solutions, periodic blow‐up wave solutions, unbounded wave solutions, kink profile solitary wave solutions, and solitary wave solutions. Relations of the traveling wave solutions are given. Some previous results are extended. Copyright © 2013 John Wiley & Sons, Ltd.     

小展弦比波的Green-Naghdi渐进模型的行波解

本文研究了小展弦比波的Green-Naghdi渐进模型. 利用平面自治系统的稳定性分析方法, 在不同的参数条件下, 讨论了它的行波系统的分岔并且给出了对应的相图, 得到了光滑周期波解, 广义扭波解, 广义反扭波解, 广义紧波解, 周期尖波解, 孤波解和孤立尖波解的精确表达式. 进一步, 通过数学软件Maple模拟了这些解.     

强非线性广义 Boussinesq 方程孤波解的波形分析及求解

上海理工大学理学院\quad 上海 200093该文建立了强非线性广义 Boussinesq 方程的耗散项、波速、渐进值与波形函数的导数之间的关系.利用适当变换和待定假设方法,作者求出了上述广义 Boussinesq 方程的扭状或钟状孤波解,还求出了以前文献中未曾提到过的余弦函数的周期波解.进一步给出了波速对波形影响的结论,即:``好'广义 Boussinesq 方程的行波当波速由小变大时,波形由钟状孤波变成余弦函数周期波解;``坏'广义 Boussinesq 方程的行波当波速由小变大时,波形由余弦函数周期波解变成钟状孤波.     

Exact solitary wave solutions of nonlinear wave equations

The hyperbolic function method for nonlinear wave equations is presented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Gr?bner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.     

Wave Surface Identification Based on Stereo Vision and Wave Theory: an Initial Attempt北大核心CSCD

波高是波浪信息最基本的元素,对波高的精确测量无论是对波浪理论的研究还是数值方法的拓展,都起着指导和验证的作用。文中基于双目立体视觉原理自主搭建了波面光学测量系统,突破了传统测量设备如浪高仪等单点测量的局限性,并将波浪理论融入到数据后处理方法中,对常用的单纯依赖图像的光学测量方法进行了改进。通过在拖曳水池中对单向规则波瞬时波面的识别和重构,并将结果与浪高仪以及理论来波参数进行了对比验证,结果表明该测量系统在大范围波面的测量中误差在1%左右,最后对其在非规则的来波下进行了初步尝试。     

Transversal wave maps and transversal exponential wave maps

Transversal wave maps and wave maps are different. There are wave maps which are not transversal wave maps, and vice versa. However, if f is a wave map under certain circumstance, then f is a transversal wave map. We show that if f is a transversal exponential wave map, then the associated energy–momentum is transversally conserved. We finally obtain the relationship among transversal wave maps, transversal exponential wave maps and certain second order symmetric tensors.     

Third order approximation to capillary gravity short crested waves with uniform currents

A third-order analytical solution for the capillary gravity short crested waves with uniform current (the main current direction is along the vertical wall) in front of a vertical wall is derived through a perturbation expanding technique. The validity and advantage of the new solution were proved by comparing the results of wave profiles and wave pressures with those of Huang and Jia [H. Huang, F. Jia, The patterns of surface capillary gravity short-crested waves with uniform current fields in coastal waters, Acta Mech. Sinica 22 (2006) 433–441] and Hsu [J.R.C. Hsu, Y. Tsuchiya, R. Silvester, Third-order approximation to short-crested waves, J. Fluid Mech 90 (1979) 179–196]. The important influences of currents on the wave profiles, wave frequency, the ratio of maximum crest height to the total wave height, and wave pressure are investigated for both small-scale (for example, the incident wave wavelength is 9.35 cm) and larger-scale (for example, the incident wave wavelength is 5 m) short crested wave. By numerical computation, we find wave frequency of short crested wave system is greatly affected by incident wave amplitude, incident angle, water depth, surface tension coefficient and the strength of the currents for small-scale incident wave. Furthermore, for the larger-scale short crested wave system, the higher-order solution with uniform current is particularly important for the prediction of wave profile and wave pressure for different water depth and incident angle. Computational results show that with the increase of the current speed, the crests of wave profile and wave pressure become more and more steep. In some cases, the crest value of wave pressure with strong current would be larger about six times than that of no current. Therefore, ocean engineers should consider the short crested wave-current load on marine constructs carefully.     

Periodic Wave Solutions and Their Limits for the Modified Kd V–KP Equations

In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified Kd V–KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions.