共查询到18条相似文献,搜索用时 62 毫秒
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讨论了允许二阶广义条件对称的四阶非线性发展方程.通过广义条件对称方法得到了其对称约化和精确解. 相似文献
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运用广义条件对称方法对径向对称的多孔介质方程进行了对称约化.确定了允许二阶广义条件对称的方程形式,并给出了方程相应的不变解. 相似文献
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本文考虑具强退缩性的非线性扩散方程的第一初边值问题。在一定的结构条件下证明了广义解具有有限传播速度。该条件在某种意义下不可改进。 相似文献
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讨论了带有热源项的非线性扩散方程.通过一种直接简洁的方法得到了几种精确解.该方法可用于更高阶演化方程的求解问题. 相似文献
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研究了一类非线性积分———微分反应扩散方程.在适当的条件下,利用微分不等式理论,讨论了退化解具有两个交叉解的初值问题解的渐近性态. 相似文献
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本文将微分方程的Lie变换群方法推广到差分方程,给出了三类非线性差分方程的不变变换,利用这种变换由差分方程的平凡解得到非平凡的单参数解族。 相似文献
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(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
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Zhenya YAN Institute of Mathematical Science Dalian University of Technology Dalian China e-mail: zhanghq@dlut. edu.cn 《Communications in Nonlinear Science & Numerical Simulation》2000,(1)
IntroductionDuring the study of water wave, many completely iategrable models were derived, such as(1+1)-dimensional KdV equation, MKdV equation, (2+1)-dimensional KdV equation, Boussinesq equation and WBK equations etc. Many properties of these models had been researched,such as BAcklund transformation (BT), converse rules, N-soliton solutions and Painleve property etc.II--8]. In this paper, we would like to consider (2+1)-dimensional variable coefficientgeneralized KP equation which … 相似文献
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运用常微分方程定性理论的相平面分析方法讨论了Hux ley方程,得到了有关其行波解的一些结果. 相似文献
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把内禀对称群分析方法推广应用于(2+2)维非线性微分-差分mToda方程.通过得到的对称,解相应的特征方程,对该方程进行了相似约化.最后通过反变换,构造了几类精确解。 相似文献
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N. A. Kudryashov 《Regular and Chaotic Dynamics》2008,13(3):234-238
The generalized Kuramoto-Sivashinsky equation in the case of the power nonlinearity with arbitrary degree is considered. New
exact solutions of this equation are presented.
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非线性偏微分方程的约化和精确解 总被引:3,自引:0,他引:3
§ 1 IntroductionSeeking the exact solutions of the nonlinear partial differential equation is one of thevery importantsubjectin PDE research.Up to now,many methods offinding the exact so-lutions for NLPDE are constructed,such as inverse scattering transformation(IST) [1 ] ,Liepoint symmetry and similar reductions[2 ,3] ,B cklund[4— 6] and Cole-Hofe transformations,Hirota s bilinear method[7] ,the homogeneous balance method[8,9] ,tanh function method[1 0 ]and so on.In this paper,we giv… 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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Lie symmetry group method is applied to study the affine heat equation for surface. Its symmetry groups and corresponding optimal systems are determined, and group-invariant solutions associated to the symmetries are obtained and classified. 相似文献