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(2＋1)维拟线性抛物方程和不变子空间 被引量：2

( 2 +1) -Dimensional Quasilinear Parabolic Equation and Invariable Subspace
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摘要 运用条件Lie-Ba¨cklund对称与不变子空间理论相结合的方法研究(2+1)维拟线性抛物方程3种形式的广义泛函分离变量解,即广义泛函多项式形式解、广义泛函三角函数形式解和广义泛函指数形式解,并对方程进行完全分类,得到了精确解中未知函数满足的动力系统. Utilizing conditional Lie-Ba¨cklund symmetry associated with invariable subspace theory,we studied three types of generalized functional separation variable solutions for（2 ＋ 1）-dimensional quasilinear parabolic equation,that is,generalized functional polynomial type solution,generalized functional trigonometric function type solution and generalized functional exponent type solution.As a result,a complete classification of the quasilinear equation was obtained.At the same time,we obtained the dynamic system satisfied by the unknown function among the exact solution.
作者 左苏丽 李吉娜
机构地区 西北大学数学系
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2011年第1期16-20,共5页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10671156) 陕西省教育厅科研基金(批准号:2010JK866)
关键词 (2+1)维拟线性抛物方程 不变子空间 泛函分离变量 精确解 （2＋1）-dimensional quasilinear parabolic equation invariant subspace functional separation variable exact solution
分类号 O175.2 [理学—基础数学]
  • 相关文献

参考文献15

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同被引文献13

  • 1唐亚宁,徐伟,李伟.推广的BBM方程行波解[J].西北大学学报（自然科学版）,2006,36(4):525-528. 被引量：5
  • 2QU C Z,LI L,DON L Z.Exact solutions and generalized conditional symmetries to(n+1)-dimensional nonlinear diffu-sion equations with source term[J].Physcics Letters A,2005,343:139-147.
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  • 4GALAKTIONOV V A,SVISHCHEVSKII S R.Exact solutions and invariant subspaces of nonlinear partial differentialequations in mechanics and physics[M].London:Boca Raton,2007.
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  • 6SVISHCHEVSKII S R.Invariant linear subspaces and exact solutions of nonlinear evolution equations[J].J Nonl MathPhys,1996(3):164-169.
  • 7SVISHCHEVSKII S R.Nonlinear differential operators of the first and second order possessing invariant spaces ofmaximal dimension[J].Theor Math Phys,1995,105:198-207.
  • 8ZHU Chun-Rong,QU Chang-Zheng.Classification and Reduction of Generalized Thin Film Equations[J].Communications in Theoretical Physics,2009,52(9):403-410. 被引量：8
  • 9夏亚荣.差分方程的不变子空间[J].齐齐哈尔大学学报（自然科学版）,2010,26(2):74-78. 被引量：1
  • 10Shoufeng SHEN,Changzheng QU,Yongyang JIN,Lina JI.Maximal Dimension of Invariant Subspaces to Systems of Nonlinear Evolution Equations[J].Chinese Annals of Mathematics,Series B,2012,33(2):161-178. 被引量：13

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吉林大学学报（理学版）
2011年 第1期

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