Generalized Buchdahl equations as Lie–Hamilton systems from the 'book' and oscillator algebras: quantum deformations and their general solution

Generalized Buchdahl equations as Lie–Hamilton systems from the 'book' and oscillator algebras: quantum deformations and their general solution

We revisit the nonlinear second-order differential equations $ \ddot{x}(t) = a (x)\dot{x}(t)^2+b(t)\dot{x}(t), $ where $ a(x) $ and $ b(t) $ are arbitrary functions on their argument from the perspective of Lie–Hamilton systems. For the particular choice $ a(x) = 3/x $ and $ b(t) = 1/t $, these eq...

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Bibliographic Details
Main Authors: Rutwig Campoamor-Stursberg, Eduardo Fernández-Saiz, Francisco J. Herranz
Format: Article
Language:English
Published: AIMS Press 2025-03-01
Series:AIMS Mathematics
Subjects:
buchdahl equations
nonlinear equations
book lie algebra
oscillator lie algebra
lie systems
lie–hamilton systems
poisson–hopf algebras
quantum groups
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2025315
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