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非线性发展方程的一维最优系统(英文) 被引量：2

One-parameter optimal systems for the nonlinearevolution equation
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摘要 系统地研究了来自于射影几何中平面曲线运动的1+1维非线性方程的对称代数。发现此方程有一个七维对称群并且其对称代数的一维最优子代数有21个元素,通过寻找在群的伴随作用下的代数不变量,证明了该最优系统的最优性。 The symmetry algebras of 1+1 dimensional nonlinear evolution equation arising from the motion of plane curve in affine geometry are systematically studied.It is found that the equation admits a sevendimensional symmetry group H1 and there are twentyone elements in the oneparameter optimal system of the symmetry algebras.The optimality of oneparameter optimal system θ1 is established by finding some algebraic invariants under the ajoint actions of the group H1.
作者 刘若辰 何文丽 张顺利 屈长征
机构地区 西北大学数学系
出处 《西北大学学报（自然科学版）》 CAS CSCD 北大核心 2003年第4期383-388,共6页 Journal of Northwest University（Natural Science Edition）
基金 supported under Natural Science Foundation grant of Shannxi(KC972 0 4)
关键词 对称李群 最优系统 伴随表示 非线性发展方程 Lie group of symmetry optimal system adjoint representation nonlinear evolution equation
分类号 O175.24 [理学—基础数学]
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参考文献5

  • 1OVSIANNIKOV L V. Group Analysis of Differential Equations[M]. New York :Academic Press, 1982.
  • 2OLVER P J. Applications of Lie Groups to Differential Equation[M]. New York :Springer Verlag, 1986.
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同被引文献29

  • 1FU Zun-tao, LIU Shi-kuo, LIU Shi-da, et al. The JEFE method and periodic solutions of two kinds of nonlinear wave equations[J]. Communications in Nonlinear Science and Numerical Simulation,2003, (8) :67-75.
  • 2CHEN Yong, LI Biao,ZHANG Hong-qing. Exact solutions for two nonlinear wave equations with nonlinear terms of any order[J]. Communications in Nonlinear Science and Numerical Simulation ,2005 , (10) :133-138.
  • 3CHOW S N, HALE J K. Method of Bifurcation Theory[M]. New York : Springer-Verlag, 1981.
  • 4PERKO L. Differential Equations and Dynamical Systems[M]. New York : Springer-Verlag, 1991.
  • 5DOGAN K. A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation[J]. Applied Mathematics and Computation, 2004,(149) :833-841.
  • 6YAN C. Regularized long wave equations and inverse scattering transform [J]. J Math Phys, 1993, ( 24 ) :2 618-2 630.
  • 7LI Ji-bin, LI Hong, LI Shu-min. Bifurcations of travelling wave solutions for the generalized Kadomtsev-Petviashili equation [J]. Chaos Solitons and Fractals, 2004, ( 20 ) :725-734.
  • 8SHEN Jian-wei, XU Wei, LEI You-ruing. Smooth and non-smooth travelling waves in a nonli-nearly dispersive Boussinesq equation [J]. Chaos Solitons and Fractals,2005, (23) : 117-130.
  • 9Vakhnenko V,Parkes E,Michtchenko A. The Vakhnenko equation from the view point of the inverse scattering method for the KdV equation[J].Int J Diff Eqns Appl,2006,(04):429-449.
  • 10Vakhnenko V,Parkes E,Morrison A. A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation[J].Chaos Solitons and Fractals,2003,(04):683-692.

引证文献2

二级引证文献6

西北大学学报（自然科学版）
2003年 第4期

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