THE EFFECTS OF SYMMETRY-BREAKING FUNCTIONS ON THE ERMAKOV-PINNEY EQUATION

Applicable Analysis and Discrete Mathematics

article

R.M. Morris¹  P.G.L. Leach² 

[1] Department of Mathematics, Durban University of Technology;Institute of Systems Science and Department of Mathematics, Durban University of Technology;School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001 Durban 4000

关键词: Ermakov-Pinney Equation;    Lie point symmetries;   

DOI  :  10.2298/AADM161106029M

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

The Ermakov-Pinney Equation,x¨ + ω2x =h2x3,has a varied provenance which we briefly delineate. We introduce timedependent functions in place of the ω2and h2. The former has no effectupon the algebra of the Lie point symmetries of the equation. The latterdestroys the sl(2, <) symmetry and a single symmetry persists only whenthere is a specific relationship between the two time-dependent functions introduced. We calculate the form of the corresponding autonomous equationfor these cases.

【 授权许可】

Unknown