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In recent years there have been existence studies on the extensive of homoclinic orbits for mearly dissipative PDEs,which are chosely related to chaos.In this work,we consider the perturbe 相似文献
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发展方程的时间依赖对称的Lie代数结构马文秀(复旦大学数学研究所,上海200433)THELIEALGEBRASTRUCTURESOFTIMEDEPENDENTSYMMETRIESOFEVOLUTIONEQUATIONS¥MAWENXIU(Insti... 相似文献
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本文生成了一族Liouville可积的Hamilton相流彼此可交换的有限维Hamilton系统,并且给出了一串对合的显式公共运动积分及其一组对合的显式生成元. 相似文献
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马文秀 《数学物理学报(B辑英文版)》1990,(3)
The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n≤3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part. 相似文献
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马文秀 《数学的实践与认识》1988,(3)
本文研究了无最小正周期的周期函数的一般性质,给出了这种函数的一般构造方法,并讨论了许多特殊情形。由此,产生了各种形式的无最小正周期的周期函数。 相似文献
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广义Pochhammer-Chree方程的显式精确孤波解 总被引:9,自引:0,他引:9
首先对广义Pochhammer-Chre方程(PC方程)utt-uttxx+ruxxt-(a1u+a2u2+a3u3)xx=0(r≠0)(Ⅰ)的孤波解u(ξ)建立了公式∫-∞+∞[u'(ξ)]2dξ=1/12rv(C+-C-)3[3a3(C++C-)+2a2]。由此推知:广义PC方程(Ⅰ)不可能有钟状孤波解,只可能有扭状孤波解;而广义PC方程utt-uttxx-(a1u+a2u2+a3u3)xx=0(Ⅱ)可能既有钟状孤波解又有渐近值满足3a3(C++C-)+2a2=0的扭状孤波解。进一步求出了广义PC方程(Ⅰ)的扭状孤波解,求出了广义PC方程(Ⅱ)的钟状孤波解和渐近值满足2a3(C++C-)+2a2=0的扭状孤波解。最后给出了广义PC方程utt-uttxx-(a1u+a3u3+a5u5)xx=0(Ⅲ)的显式孤波解。 相似文献
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Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation 下载免费PDF全文
Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a (3+1)-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented. 相似文献
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提出了基于Lax矩阵的构造双约束孤立子流的可积形变的新方法.作为应用,导出了双约束KdV流和双约束mKdV流的可积形变,并给出了这些形变的Lax表示、r-矩阵和守恒积分. 相似文献
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In this paper, starting from the combination of two in volutive systems, we consider separately some systems of polynomial functions:{Im(1)=Bm+Rm}m=0∞, {Im(2)=Bm+Sm}m=0∞, {Im(3)=Bm+Tm}m=0∞ and so on; and analyse carefully the sufft cient and necessary conditions of the involution of three systems of functions {Im(i)}m=0∞(1≤i≤3) with general coefficients.Furthermore,we present concrete forms of the involutive systems hidden in {Im(i)}m=0∞(1≤i≤3);and thus obtain six kinds of nontrivial involutive systems of functions, which include a few involutive systems discussed inthe literature. Based upon these involutive systems, we can generate a lot of new finite-dimensional Hamiltonian systems which are completely integrable in the sense of Liouville. 相似文献