Classification of ordinary differential equations by conditional linearizability and symmetry

被引:8
作者
Mahomed, F. M. [1 ]
Qadir, Asghar [2 ]
机构
[1] Univ Witwatersrand, Ctr Differential Equat Continuum Mech & Applicat, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
[2] Natl Univ Sci & Technol, Ctr Adv Math & Phys, Islamabad, Pakistan
关键词
Symmetry algebra; Linearizability; Conditional linearizability; Classification; LINEARIZATION CRITERIA; GEOMETRY; SYSTEMS; POINT;
D O I
10.1016/j.cnsns.2011.06.012
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Lie's invariant criteria for determining whether a second order scalar equation is linearizable by point transformation have been extended to third and fourth order scalar ordinary differential equations (ODES). By differentiating the linearizable by point transformation scalar second order ODE (respectively third order ODE) and then requiring that the original equation holds, what is called conditional linearizability by point transformation of third and fourth order scalar ODEs, is discussed. The result is that the new higher order nonlinear ODE has only two arbitrary constants available in its solution. One can use the same procedure for the third and fourth order extensions mentioned above to get conditional linearizability by point or other types of transformation of higher order scalar equations. Again, the number of arbitrary constants available will be the order of the original ODE. A classification of ODEs according to conditional linearizability by transformation and classifiability by symmetry are proposed in this paper. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:573 / 584
页数:12
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