共查询到19条相似文献,搜索用时 203 毫秒
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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
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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
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A. D. Smirnov 《Optics and Spectroscopy》2002,93(5):678-681
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
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Cheng-Shi Liu 《Foundations of Physics》2011,41(5):793-804
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
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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
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W. Strampp 《Physica D: Nonlinear Phenomena》1982,6(1):113-118
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
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Numerical study on characteristics of nitrogen discharge at high pressure with induced plasma 下载免费PDF全文
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 (A3∑u+), N2 (a1∑u-)) 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
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《Journal of Nonlinear Mathematical Physics》2013,20(2):117-125
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
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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
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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