Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

DOI10.1016/j.physleta.2018.03.037zbMath1398.34050OpenAlexW2794602766WikidataQ130054377 ScholiaQ130054377MaRDI QIDQ1990200

Maria V. Demina

Publication date: 25 October 2018

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2018.03.037

zbMATH Keywords

Duffing oscillatorDarboux polynomialsDuffing-van der Pol oscillatorinvariant algebraic curvesLiouvillian first integrals

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Cites Work

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• From Laurent series to exact meromorphic solutions: The Kawahara equation
• Duffing-van der Pol-type oscillator systems
• Integrability of dynamical systems: algebra and analysis
• Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation
• On elliptic solutions of nonlinear ordinary differential equations
• A new algorithm for finding rational first integrals of polynomial vector fields
• A note on Liouvillian first integrals and invariant algebraic curves
• Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations
• Abel differential equations admitting a certain first integral
• Invariant algebraic curves for Liénard dynamical systems revisited
• Hypergeometric first integrals of the Duffing and van der Pol oscillators
• A simple and unified approach to identify integrable nonlinear oscillators and systems
• Liouvillian First Integrals of Differential Equations
• Invariant algebraic curves and conditions for a centre
• Asymptotic behaviour and expansions of solutions of an ordinary differential equation
• New aspects of integrability of force-free Duffing–van der Pol oscillator and related nonlinear systems
• On the non-integrability of a family of Duffing-van der Pol oscillators
• Liouvillian first integrals for Liénard polynomial differential systems
• The role of algebraic solutions in planar polynomial differential systems

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