共查询到20条相似文献,搜索用时 93 毫秒
1.
本文研究具有受迫性的广义二维KdV-Burgers方程的周期行波解,为了获得周期行波解的存在唯一性定理,使唤用特定系数法和Schauder不动点定理获得了受迫广义KdV-Burgers方程周期行波解存在唯一性的条件.并获得了周期行波解的一些先验估计式. 相似文献
2.
3.
mKdV方程的对称与群不变解 总被引:1,自引:0,他引:1
主要考虑mKdV方程的一些简单对称及其构成的李代数,并利用对称约化的方法将mKdV方程化为常微分方程,从而得到该方程的群不变解,这是对该方程群不变解的进一步扩展. 相似文献
4.
提出一种求解线性矩阵方程AX+XB=C双对称解的迭代法.该算法能够自动地判断解的情况,并在方程相容时得到方程的双对称解,在方程不相容时得到方程的最小二乘双对称解.对任意的初始矩阵,在没有舍入误差的情况下,经过有限步迭代得到问题的一个双对称解.若取特殊的初始矩阵,则可以得到问题的极小范数双对称解,从而巧妙地解决了对给定矩... 相似文献
5.
利用广义条件对称,考虑非线性反应扩散方程的精确解,对应于不同的参数讨论,得到相应的方程及其允许的广义条件对称,进而得到方程的精确解. 相似文献
6.
7.
8.
9.
在共轭梯度思想的启发下,本文给出了迭代算法求解约束矩阵方程AXB+CXD=F的对称解及其最佳逼近.应用迭代算法,矩阵方程AXB+CXD=F的相容性可以在迭代过程中自动判断.当矩阵方程AXB+CXD=F有对称解时,在有限的误差范围内,对任意初始对称矩阵X1,运用迭代算法,经过有限步可得到矩阵方程的对称解;选取合适的初始迭代矩阵,还可以迭代出极小范数对称解.而且,对任意给定的矩阵X0,矩阵方程AXB+CXD=F的最佳逼近对称解可以通过迭代求解新的矩阵方程A(X)B+C(X)D=(F)的极小范数对称解得到.文中的数值例子证实了该算法的有效性. 相似文献
10.
(2+1)维广义Burgers 方程的Lie点对称, 相似约化和精确解 总被引:2,自引:1,他引:1
讨论了(2+1)维广义Burgers方程.通过Lie群方法求出了该方程的李点对称,并利用李点对称将方程进行相似约化,求出了(2+1)维广义Burgers方程的几种精确解.该方法可以用于研究更高阶的偏微分方程. 相似文献
11.
In this paper, the pseudo-spectral approximations for a class of the Kdv-Burgers type equation is presented. Convergence and stability of the approximation have been proved by Sobolev‘s inequalities and the bounded extensive method of the nonlinear function. Finally, the numerical examples are proposed. 相似文献
12.
Zhongxin Zhang 《Journal of Mathematical Analysis and Applications》2010,361(1):96-107
This paper is devoted to a general similarity boundary layer equation for power-law fluids, which includes many important similarity boundary layer problems such as the Falker-Skan equation and the magnetohydrodynamic boundary layer equation which arises in the study of self-similar solutions of the two-dimensional steady laminar boundary layer flow for an incompressible electrically conducting power-law fluids along an isolated surface in the presence of an exterior magnetic field orthogonal to the flow. By a rigorous mathematical analysis, the uniqueness, existence and nonexistence results for convex solutions, normal convex solutions and generalized convex solutions to the general similarity boundary layer equation are established. Also the asymptotic behavior of the normal convex solutions at the infinity are displayed. 相似文献
13.
二维RLW方程和二维SRLW方程的显式精确解 总被引:2,自引:0,他引:2
本文讨论了二维RLW方程和二维SRLW方程孤立波解的性态,通过直接积分的方法求出了这两个方程的显式精确孤立波解,并通过选取初始条件的方法求出了二维RLW方程和二维SRLW方程的另一类精确行波解. 相似文献
14.
Existence of kink and unbounded traveling wave solutions of the Casimir equation for the Ito system 下载免费PDF全文
This paper study the traveling wave solutions of the Casimir equation for the Ito system. Since the derivative function of the wave function is a solution of a planar dynamical system, from which the exact parametric representations of solutions and bifurcations of phase portraits can be obtained. Thus, we show that corresponding to the compacton solutions of the derivative function system, there exist uncountably infinite kink wave solutions of the wave equation. Corresponding to the positive or negative periodic solutions and homoclinic solutions of the derivative function system, there exist unbounded wave solutions of the wave function equation. 相似文献
15.
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan‘s, Xie‘s and Yan‘s results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations. 相似文献
16.
Fang Yan Haihong Liu Zengrong Liu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(7):2824-2832
By using methods from dynamical systems theory, this paper researches the bifurcation and exact travelling wave solutions for the modified Benjamin-Bona-Mahoney (mBBM) equation. Implicit exact parametric representations of all travelling wave solutions as well as some explicit analytic solutions are given. Specially, breaking wave solutions are obtained, which KdV equation does not include. 相似文献
17.
18.
Group-invariant solutions, non-group-invariant solutions and conservation laws of Qiao equation 下载免费PDF全文
This paper considers a completely integrable nonlinear wave equation which is called Qiao equation. The equation is reduced via Lie symmetry analysis. Two classes of new exact group-invariant solutions are obtained by solving the reduced equations. Specially, a novel technique is proposed for constructing group-invariant solutions and non-group-invariant solutions based on travelling wave solutions. The obtained exact solutions include a set of traveling wave-like solutions with variable amplitude, variable velocity or both. Nonlocal conservation laws of Qiao equation are also obtained with the corresponding infinitesimal generators. 相似文献
19.
Wen-Xiu MA 《Frontiers of Mathematics in China》2019,14(3):619-629
Abundant exact interaction solutions, including lump-soliton, lump-kink, and lump-periodic solutions, are computed for the Hirota-Satsuma-Ito equation in (2+1)-dimensions, through conducting symbolic computations with Maple. The basic starting point is a Hirota bilinear form of the Hirota-Satsuma-Ito equation. A few three-dimensional plots and contour plots of three special presented solutions are made to shed light on the characteristic of interaction solutions. 相似文献
20.
In this paper, many types of exact solutions of a first-order nonlinear ordinary differential equation called Fan sub-equation, is further investigated by using bifurcation method of dynamical systems. As a result, more types of exact solutions to Sawada-Kotera (SK) equation are obtained, which include more general soliton solutions, kink solutions, triangular function solutions, Jacobian elliptic function solutions with double periods and so on. 相似文献