Dynamical Studies of Equations from the Gambier Family

Symmetry Integrability and Geometry-Methods and Applications

article

Partha Guha¹  Anindya Ghose Choudhury²  Basil Grammaticos³ 

[1] S.N. Bose National Centre for Basic Sciences;Department of Physics, Surendranath College;Université Paris VII-Paris XI

关键词: Gambier equation;    Riccati sequence of dif ferential equations;    Milney–Pinney equation;    folding transformation;    superintegrability;   

DOI  :  10.3842/SIGMA.2011.028

来源: National Academy of Science of Ukraine

【 摘 要 】

We consider the hierarchy of higher-order Riccati equations and establish their connection with the Gambier equation. Moreover we investigate the relation of equations of the Gambier family to other nonlinear differential systems. In particular we explore their connection to the generalized Ermakov-Pinney and Milne-Pinney equations. In addition we investigate the consequence of introducing Okamoto's folding transformation which maps the reduced Gambier equation to a Liénard type equation. Finally the conjugate Hamiltonian aspects of certain equations belonging to this family and their connection with superintegrability are explored.

【 授权许可】

Unknown