City Research Online

Abstract

We investigate an interacting Pais–Uhlenbeck oscillator with a particular polynomial self-interaction with derivative coupling and analyse its classical dynamics from a geometric and numerical point of view. We show that the resulting fourth-order equation of motion admits a conformal bi-Hamiltonian formulation, possesses a non-trivial set of Lie symmetries and we demonstrate the existence of bounded and regular trajectories in representative parameter regimes. By establishing an explicit correspondence with an integrable generalised Hénon–Heiles system, we show that the interacting higher–derivative dynamics inherits the integrability properties of the latter. This connection allows us to construct a second conserved Hamiltonian function, to clarify the geometric origin of separability, and to obtain explicit classical solutions in terms of elliptic functions. Our results provide a concrete example of an interacting higher-derivative system for which integrability can be established explicitly and for which families of bounded and periodic classical solutions can be constructed. At the same time, the model also admits unbounded trajectories outside these regular parameter regimes, so that the periodic behaviour should be understood as an integrable island rather than as a global stability statement.

Publication Type:	Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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