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1.
一类非线性演化方程新的显式行波解   总被引:37,自引:4,他引:33       下载免费PDF全文
借助Mathematica软件,采用三角函数法和吴文俊消元法,获得了一类非线性演化方程utt+auxx+bu+cu3=0的三组行波解,其中包括新的行波解、扭状孤波解和钟状孤波解.从而作为该方程的特例,如Duffing方,Klein-Gordon方程、Landau-Ginburg-Higgs方程和4方程等也都获得了相应的若干行波解.这种方法也适用于其他非线性方程. 关键词:  相似文献   

2.
一类五阶非线性演化方程的新孤波解   总被引:3,自引:0,他引:3       下载免费PDF全文
徐炳振  李悦科  阎循领 《物理学报》1998,47(12):1946-1951
利用齐次平衡法给出了一类较广泛的五阶非线性演化方程的孤波解,数学物理中著名的Kaup-Kupershmidt方程、Caudrey-Dodd-Gibbon-Sawada-Kotera方程和五阶Korteweg-de-Vries方程等都可作为该方程的特殊情形而得到相应的孤波解. 关键词:  相似文献   

3.
具5次强非线性项的波方程新的孤波解   总被引:11,自引:1,他引:10       下载免费PDF全文
提出一种新的函数变换法,并与直接积分法相结合简便地求出了Lienard方程、广义PC方程以及力学中重要的一类非线性波方程等几类具5次强非线性项的波方程的四类显示精确孤波解.本方法同样适用于求解其他具有更高次非线性项的非线性方程. 关键词: 函数变换法 孤波解 直接积分法 非线性波方程  相似文献   

4.
非线性孤子方程的齐次平衡法   总被引:152,自引:0,他引:152       下载免费PDF全文
范恩贵  张鸿庆 《物理学报》1998,47(3):353-362
齐次平衡法是求非线性孤子方程孤波解的一种十分有效的方法.对齐次平衡法的一些关键步骤进行拓广使用,获得了非线性孤子方程一批新的具有更为丰富形式的精确解,孤波解仅是其中的一种特殊情形,使得结果更加完美. 关键词:  相似文献   

5.
朱佐农 《物理学报》1992,41(7):1057-1062
本文研究了推广的KdV方程 ut+2μuux+v3x+δu5x=0(μvδ≠0) (1)的精确孤子解,得到了(1)式的一些新的孤波解,对文献[10]的若干结论作了补充与修正。 关键词:  相似文献   

6.
一类非线性演化方程的新多级准确解   总被引:5,自引:0,他引:5       下载免费PDF全文
付遵涛  刘式适  刘式达 《物理学报》2003,52(12):2949-2953
在Lamé方程和新的Lamé函数的基础上,应用小扰动方法和Jacobi椭圆函数展开法求解一类非线性演化方程(如mKdV方程,非线性Klein-Gordon方程Ⅱ等),获得多种新的多级准确解 .这些多级准确解对应着不同形式的周期波解.这些解在极限条件下可以退化为多种形式的孤 立波解,如带状孤立子、钟形孤立子等. 关键词: Jacobi椭圆函数 Lam函数 多级准确解 非线性演化方程 扰动方法  相似文献   

7.
非线性波方程尖峰孤子解的一种简便求法及其应用   总被引:1,自引:0,他引:1       下载免费PDF全文
刘煜 《物理学报》2009,58(11):7452-7457
根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH(Camassa-Holm)方程、五阶KdV-like 方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解. 关键词: 非线性波方程 尖峰孤子解 待定系数法  相似文献   

8.
一类相对论性非球谐振子系统的束缚态   总被引:6,自引:0,他引:6       下载免费PDF全文
李宁  鞠国兴  任中洲 《物理学报》2005,54(6):2520-2523
给出了具有形式为12r2+A2r2的非球谐振子型标量势和矢量势 的相对论系 统在两种势相等的条件下三维Klein-Gordon方程,二维和三维Dirac方程的s波束缚态解. 关键词: 三维非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态  相似文献   

9.
三类非线性演化方程新的Jacobi椭圆函数精确解   总被引:2,自引:0,他引:2       下载免费PDF全文
吴海燕  张亮  谭言科  周小滔 《物理学报》2008,57(6):3312-3318
应用修正影射法分别求解三类非线性演化方程,即非线性Klein-Gordon方程,mKdV方程和广义Boussinesq方程,得到了一些新的Jacobi椭圆函数展开解,包括Jacobi椭圆函数解、混合Jacobi椭圆函数解、孤子解和三角函数解. 关键词: Klein-Gordon方程 mKdV方程 广义Boussinesq方程 Jacobi椭圆函数  相似文献   

10.
扩展的混合指数方法及其应用   总被引:7,自引:0,他引:7       下载免费PDF全文
徐桂琼  李志斌 《物理学报》2002,51(7):1424-1427
改进了Hereman提出的构造非线性发展方程孤波解的混合指数方法,通过将非线性发展方程孤波解的表示形式推广到实指数解或复指数解的无穷级数,得到了扩展的混合指数方法.以正则长波方程为例,说明通过扩展的混合指数方法可获得包括正则孤波解、奇异孤波解及周期解在内的诸多精确解 关键词: 孤波解 混合指数法 正则长波方程  相似文献   

11.
具有阻尼项的非线性波动方程的相似约化   总被引:8,自引:0,他引:8       下载免费PDF全文
闫振亚  张鸿庆 《物理学报》2000,49(11):2113-2117
利用Clarkson和Kruskal引入的直接约化法,给出了具有阻尼项的非线性波动方程utt-2buxxt+αuxxxx=β(unx)x(α>0,β≠0,n≥2)三种类型的相似约化.从这些约化方程的Painlevé分析表明该方程在Ablowitz的猜测意义下是不可积的.此外还获得了该方程(n=2)的4种精确类孤波解. 关键词: 波动方程 相似约化 Painlevé分析 精确解  相似文献   

12.
The molecular constants are calculated for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.  相似文献   

13.
To find exact traveling wave solutions to nonlinear evolution equations, we propose a method combining symmetry properties with trial polynomial solution to nonlinear ordinary differential equations. By the method, we obtain some exact traveling wave solutions to the Burgers-KdV equations and a kind of reaction-diffusion equations with high order nonlinear terms. As a result, we prove that the Burgers-KdV equation does not have the real solution in the form a 0+a 1tan ξ+a 2tan 2 ξ, which indicates that some types of the solutions to the Burgers-KdV equation are very limited, that is, there exists no new solution to the Burgers-KdV equation if the degree of the corresponding polynomial increases. For the second equation, we obtain some new solutions. In particular, some interesting structures in those solutions maybe imply some physical meanings. Finally, we discuss some classifications of the reaction-diffusion equations which can be solved by trial equation method.  相似文献   

14.
拍波激光加速器中的频率匹配   总被引:3,自引:0,他引:3       下载免费PDF全文
朱莳通 《物理学报》1989,38(7):1167-1171
本文从广义协变的运动方程和麦克斯韦方程出发,导出了电子等离子体波各量的解析表达式。指出△ω=2ωp的等离子体波是完全简谐的。完全共振的条件由△ω=2ω(p0)[1+(e2(A2((1)2)+(A2((2)2))/(2m2c4)+(3e2A2(1)A2(2))/(m2c4)]-1/2 给出。 关键词:  相似文献   

15.
A class of Bäcklund transformations is deduced for the diffusion equation (S(u))t = (C(u,ux))x by taking advantage of the conservative form of the equation. The transformations are used for obtaining new relations connecting various equations of the type ut = (uaux)x and ut = uauxx.  相似文献   

16.
Based on the fluid theory of plasma, a model is built to study the characteristics of nitrogen discharge at high pressure with induced argon plasma. In the model, the spices such as electron, N2+, N4+, Ar+, and two metastable states (N2 (A3u+), N2 (a1u-)) are taken into account. The model includes particle's continuity equations, electron's energy balance equation, and Poisson equation. The model is solved with a finite difference method. The numerical results are obtained and used to investigate the effect of time taken to add nitrogen gas and initially-induced argon plasma pressure. It is found that lower speeds of adding the nitrogen gas and varying the gas pressure can induce higher plasma density, and inversely lower electron temperature. At high-pressure discharge, the electron density increases when the proportion of nitrogen component is below 40%, while the electron density will keep constant as the nitrogen component further increases. It is also shown that with the increase of initially-induced argon plasma pressure, the density of charged particles increases, and the electron temperature as well as the electric field decrease.  相似文献   

17.
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa–Holm equation are distributional traveling wave solutions to the Camassa–Holm equation provided that the set u-1(c), where c is the speed of the wave, is of measure zero. In particular there are no new peakon or cuspon solutions beyond those already satisfying the Camassa–Holm equation. However, the two component Camassa–Holm equation has distinct from Camassa–Holm equation smooth traveling wave solutions as well as new distributional solutions when the measure of u-1(c) is not zero. We provide examples of such solutions.  相似文献   

18.
We prove that the set of solitary wave solutions of a generalized Kadomtsev-Petviashvili equation in two dimensions, (u t+(um+1)x+uxxx)x=uyy is stable for 0<m<4/3.  相似文献   

19.
We have calculated numerically the temporal evolution of the nonlinear reflection coefficient R of an overdense plasma layer by solving the system of partial differential equations consisting of the wave equation for the slowly varying amplitude of the electric field and the hydrodynamic equations for the ion motion, including a ponderomotive force term. In dependence of the (normalized) amplitude of the incident wave uA two regimes exist: Below a critical amplitude uA* ? 1 the reflection coefficient is approximately independent on the amplitude uA and temporally constant. In the opposite case uA>uA*, on the other hand, ‖R‖2 decreases slowly with time down to a minimum value and after that it increases rapidly to the initial value. We think, that our results are important to interpret the anomalous reflectivity observed in some experiments when strong electromagnetic waves are incident on an overdense plasma.  相似文献   

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