共查询到20条相似文献,搜索用时 15 毫秒
1.
非线性演化方程显式精确解的新算法 总被引:1,自引:0,他引:1
本文给出了一种求解非线性演化方程的新算法 .将这种算法运用于变形浅水波方程 ,获得了八组显式精确解 ,其中包括新的孤波解和周期解 .借助于 Mathematica软件 ,这种算法能够在 Computer上实现 . 相似文献
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Jibin Li 《Annals of Differential Equations》2014,(1):15-32
For the Davey-Stewartson system, the exact dark solitary wave solutions, solitary wave solutions, kink wave solution and periodic wave solutions are studied. To guarantee the existence of the above solutions, all parameter conditions are determined. The persistence of dark solitary wave solutions to the perturbed Davey-Stewartson system is proved. 相似文献
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JiBin Li 《中国科学A辑(英文版)》2008,51(9):1577-1592
Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. 相似文献
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Exact traveling wave solutions and dynamical behavior for the (n+1)-dimensional multiple sine-Gordon equation 总被引:1,自引:0,他引:1
Ji-bin LI Department of Mathematics Zhejiang Normal University Jinhua China Kunming University of Science Technology Kunming China 《中国科学A辑(英文版)》2007,(2)
Using the methods of dynamical systems for the (n 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions axe obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. 相似文献
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By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalized modified Boussinesq equation. We also discuss the boundedness of these solutions. More over, we study the correlative characteristic of the solitary-wave solutions and the periodic wave solutions along with the travelling wave velocity's variation. 相似文献
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New exact traveling wave solutions are derived for two coupled nonlinear water wave equations by using a delicate way of rank analysis two-step ansatz method. 相似文献
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Ji-bin Li 《中国科学A辑(英文版)》2007,50(2):153-164
Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking
bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of
the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are
determined.
This work was supported by the National Natural Science Foundation of China (Grant No. 11671179) and the Natural Science Foundation
of Yunnan Province (Grant No. 2005A0092M). 相似文献
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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. 相似文献
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两个非线性发展方程精确解析解的研究 总被引:6,自引:0,他引:6
对齐次平衡法进行了改进并将其应用于两个非线性发展方程中,通过一些新的假设,获得了若干精确解析解,这些解包含王和张的结论及其它新类型的解析解,如果理分式解和周期解,这种方法也可以应用于求解更多的非线性偏微分方程。 相似文献
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De-Xin Meng Xiao-Ling Gai Xin Yu Ming-Zhen Wang 《Applied mathematics and computation》2009,215(5):1744-1751
Variable-coefficient variant Boussinesq (VCVB) system is able to describe the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth. In this paper, with symbolic computation, a Lax pair associated with the VCVB system under some constraints for variable coefficients is derived, and based on the Lax pair, two sorts of basic Darboux transformations are presented. By applying the Darboux transformations, some solitonic solutions are obtained, with the relevant constraints given in the text. In addition, the VCVB system is transformed to a variable-coefficient Broer-Kaup system. Solitonic solutions and procedure of getting them could be helpful to solve the nonlinear and dispersive problems in fluid dynamics. 相似文献
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利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质. 相似文献
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Jianming Zhang Shuming Li Hongpeng Geng 《Journal of Applied Analysis & Computation》2016,6(4):1205-1210
Using the method of dynamical systems for the the generalized Radhakrishnan, Kundu, Lakshmanan equation, the existence of soliton solutions, uncountably infinite many periodic wave solutions and unbounded wave solution are obtained. Exact explicit parametric representations of the above travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. 相似文献
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In this paper, Hermitian positive definite solutions of the nonlinear matrix equation X + A^*X^-qA = Q (q≥1) are studied. Some new necessary and sufficient conditions for the existence of solutions are obtained. Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions, and the convergence analysis is also given. The theoretical results are illustrated by numerical examples. 相似文献
17.
Jerry L. Bona & Min Chen 《数学研究》2016,49(3):205-220
Studied here is the Boussinesq system $$η_t+u_x+(ηu)_x+au_{xxx}-bη_{xxt}=0,$$ $$u_t+η_x+\frac{1}{2}(u²)_x+cη_{xxx}-du_{xxt}=0,$$of partial differential equations. This system has been used in theory and practice as a
model for small-amplitude, long-crested water waves. The issue addressed is whether
or not the initial-value problem for this system of equations is globally well posed.The investigation proceeds by way of numerical simulations using a computer code
based on a a semi-implicit, pseudo-spectral code. It turns out that larger amplitudes
or velocities do seem to lead to singularity formation in finite time, indicating that the
problem is not globally well posed. 相似文献
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Solitary wave and chaotic behavior of traveling wave solutions for the coupled Schr$\ddot{o}$dinger-KdV equations 下载免费PDF全文
This paper deals with the coupled Schr$\ddot{o}$dinger-KdV equations by making use of the method of dynamical systems. We obtain some exact explicit parametric representations of the solitary wave and periodic wave solutions in the given parameter regions, and study chaotic behavior of travelling wave solutions. 相似文献
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In this paper, the two-dimensional (2D) Holf-Cole transformation with mass conservation in the frame of conformable derivative is developed, and then by introducing some exact solutions that satisfy linear differential equations and using the symbolic computation method, four exact solutions of 2D-nonlinear Navier-Stokes equations (NSEs) with the conformable time-fractional derivative are established. Some physical properties of the exact solutions are described preliminarily. Our results are the first ones on analytical study for the 2D time-fractional NSEs. 相似文献
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Zhu Yanjuan Zhang Chunhua 《Annals of Differential Equations》2005,21(1):106-110
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations. 相似文献