Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-03-22
SIGMA 7 (2011), 028, 15 pages
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
10.3842/SIGMA.2011.028
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 Li\'enard type equation. Finally the conjugate Hamiltonian aspects of certain equations belonging to this family and their connection with superintegrability are explored.
Choudhury Anindya Ghose
Grammaticos Basil
Guha Partha
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