A class of third-order nonlinear evolution equations admitting invariant subspaces and associated reductions

被引：17
|
作者：
Ye, Yujian [1 ]
Ma, Wen-Xiu [2 ]
Shen, Shoufeng [3 ]
Zhang, Danda [3 ]
机构：
[1] Hangzhou Dianzi Univ, Sch Management, Hangzhou 310018, Peoples R China
[2] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
[3] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310023, Zhejiang, Peoples R China
来源：
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2014年 / 21卷 / 01期
关键词：
evolution equation; invariant subspace; separation of variables; reduction; dynamical system; DIFFERENTIAL-EQUATIONS; MAXIMAL DIMENSION; SYMMETRY; SYSTEMS;
D O I：
10.1080/14029251.2014.894726
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
With the aid of symbolic computation by Maple, a class of third-order nonlinear evolution equations admitting invariant subspaces generated by solutions of linear ordinary differential equations of order less than seven is analyzed. The presented equations are either solved exactly or reduced to finite-dimensional dynamical systems. A number of concrete examples admitting invariant subspaces generated by power, trigonometric and exponential functions are computed to illustrate the resulting theory.
引用
收藏
页码：132 / 148
页数：17
相关论文
共 50 条
  • [21] Nonlinear evolution equations and their stationary reductions
    Fordy A.P.
    Harris S.
    Journal of Mathematical Sciences, 1999, 94 (4) : 1600 - 1610
  • [22] Quasi-invariant Gaussian measures for the cubic nonlinear Schrodinger equation with third-order dispersion
    Oh, Tadahiro
    Tsutsumi, Yoshio
    Tzvetkov, Nikolay
    COMPTES RENDUS MATHEMATIQUE, 2019, 357 (04) : 366 - 381
  • [23] Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations
    Ahmed, Waheed A.
    Zaman, F. D.
    Saleh, Khairul
    MATHEMATICS, 2017, 5 (04)
  • [24] Symmetry analysis and conservation laws of some third-order difference equations
    Folly-Gbetoula, M. K.
    Mamba, S.
    Kara, A. H.
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2018, 24 (01) : 1 - 14
  • [25] Invariant subspaces and conditional Lie-Backlund symmetries of inhomogeneous nonlinear diffusion equations
    Qu ChangZheng
    Ji LiNa
    SCIENCE CHINA-MATHEMATICS, 2013, 56 (11) : 2187 - 2203
  • [26] Conditional Lie-Backlund symmetries and invariant subspaces to nonlinear diffusion equations with source
    Ji, Lina
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2012, 391 (24) : 6320 - 6331
  • [27] On Kneser solutions of third-order delay dynamic equations
    Grace, Said R.
    Bohner, Martin
    Liu, Ailian
    CARPATHIAN JOURNAL OF MATHEMATICS, 2010, 26 (02) : 184 - 192
  • [28] Classification of nonnegative classical solutions to third-order equations
    Dai, Wei
    Qin, Guolin
    ADVANCES IN MATHEMATICS, 2018, 328 : 822 - 857
  • [29] Oscillation of Third-Order Differential Equations with Advanced Arguments
    Aldiaiji, Munirah
    Qaraad, Belgees
    Iambor, Loredana Florentina
    Rabie, Safi S.
    Elabbasy, Elmetwally M.
    MATHEMATICS, 2024, 12 (01)
  • [30] EULER CASE FOR A CLASS OF THIRD-ORDER DIFFERENTIAL EQUATION
    Al-Hammadi, A. S. A.
    MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2010, 51 : 5 - 15
12345