TY  - JOUR
AU  - Nikolić, Mladen
AU  - Rajković, Milan
PY  - 2007
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3144
AB  - The solution of a class of third order ordinary differential equations possessing two parameter Lie symmetry group is obtained by group theoretic means. It is shown that reduction to quadratures is possible according to two scenarios: (1) if upon first reduction of order the obtained second order ordinary differential equation besides the inherited point symmetry acquires at least one more new point symmetry (possibly a hidden symmetry of Type II). (2) First, reduction paths of the fourth order differential equations with four parameter symmetry group leading to the first order equation possessing one known (inherited) symmetry are constructed. Then, reduction paths along which a third order equation possessing two-parameter symmetry group appears are singled out and followed until a first order equation possessing one known (inherited) symmetry are obtained. The method uses conditions for preservation, disappearance and reappearance of point symmetries.
T2  - Nonlinear Dynamics
T1  - Integration of third order ordinary differential equations possessing two-parameter symmetry group by Lies method
VL  - 48
IS  - 1-2
SP  - 17
EP  - 27
DO  - 10.1007/s11071-006-9040-1
ER  - 

@article{
author = "Nikolić, Mladen and Rajković, Milan",
year = "2007",
abstract = "The solution of a class of third order ordinary differential equations possessing two parameter Lie symmetry group is obtained by group theoretic means. It is shown that reduction to quadratures is possible according to two scenarios: (1) if upon first reduction of order the obtained second order ordinary differential equation besides the inherited point symmetry acquires at least one more new point symmetry (possibly a hidden symmetry of Type II). (2) First, reduction paths of the fourth order differential equations with four parameter symmetry group leading to the first order equation possessing one known (inherited) symmetry are constructed. Then, reduction paths along which a third order equation possessing two-parameter symmetry group appears are singled out and followed until a first order equation possessing one known (inherited) symmetry are obtained. The method uses conditions for preservation, disappearance and reappearance of point symmetries.",
journal = "Nonlinear Dynamics",
title = "Integration of third order ordinary differential equations possessing two-parameter symmetry group by Lies method",
volume = "48",
number = "1-2",
pages = "17-27",
doi = "10.1007/s11071-006-9040-1"
}

Nikolić, M.,& Rajković, M.. (2007). Integration of third order ordinary differential equations possessing two-parameter symmetry group by Lies method. in Nonlinear Dynamics, 48(1-2), 17-27.
https://doi.org/10.1007/s11071-006-9040-1

Nikolić M, Rajković M. Integration of third order ordinary differential equations possessing two-parameter symmetry group by Lies method. in Nonlinear Dynamics. 2007;48(1-2):17-27.
doi:10.1007/s11071-006-9040-1 .

Nikolić, Mladen, Rajković, Milan, "Integration of third order ordinary differential equations possessing two-parameter symmetry group by Lies method" in Nonlinear Dynamics, 48, no. 1-2 (2007):17-27,
https://doi.org/10.1007/s11071-006-9040-1 . .