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一类拟线性方程三角形式不变子空间的研究 被引量：1

The study of trigonometric invariant subspace to a class of quasilinear equation
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摘要 讨论一类含有F[u]=sum (aijDixuDjxu) from i+j=k形式的拟线性方程所满足的三角形式的不变子空间.将假设的正余弦形式的不变子空间代入演化方程,对不同的k值进行分析对比.证明了对于这类方程,当k为偶数时,若方程满足一定维数的余弦形式的不变子空间,则必满足余弦/正弦形式的不变子空间. To study the kind of quasilinear equations which with the form of F[u]=sum （aijDixuDjxu） from i＋j=k.Utilize the trigonometric invariant subspace on k with different values to analysis the different coefficient conditions.When k is even,the equations allow the cos/sin-invariant subspace if this equations allow cos-invariant subspace.
作者 高晓琴 谢离丽
机构地区 西北大学数学系 西北大学非线性研究中心
出处 《纺织高校基础科学学报》 CAS 2012年第1期48-50,共3页 Basic Sciences Journal of Textile Universities
关键词 二次算子 不变子空间 三角形式不变子空间 精确解 quadratic operator of the second order invariant subspace trigonometric invariant subspaceexact solutions
分类号 O175.2 [理学—基础数学]
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参考文献9

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共引文献5

同被引文献8

  • 1Changzheng Qu.Group classification and generalized conditional symmetry reduction of the nonlinear diffusion-convection equation with a nonlinear source. Studies in Applied Mathematics . 1997
  • 2Victor A. Galaktionov.Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities. Proceedings of the Royal Society of Edinburgh, Section: A Mathematics . 1995
  • 3A.S. Fokas,Q.M. Liu.Nonlinear interaction of traveling waves of nonintegrable equations. Physical Review Letters . 1994
  • 4R.Z. Zhdanov.Conditional Lie-B\"acklund symmetry and reduction of evolution equations. J. Phys. A, Math. Gen . 1995
  • 5Changzheng Qu,Chunrong Zhu.Classification of coupled systems with two-component nonlinear diffusion equations by the invariant subspace method. J. Phys. A, Math. Theor . 2009
  • 6GALAKTIONOV V A,SVIRSHCHEVSKII S R.Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics. . 2007
  • 7左苏丽,黄晴,王丽真,李吉娜.非线性扩散方程和不变子空间[J].西北大学学报（自然科学版）,2011,41(1):5-7. 被引量：1
  • 8MA Wen-Xiu.A refined invariant subspace method and applications to evolution equations[J].Science China Mathematics,2012,55(9):1769-1778. 被引量：21

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纺织高校基础科学学报
2012年 第1期

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