On the geometric and analytical properties of the anharmonic oscillator

DOI10.1016/j.cnsns.2024.107875arXiv2401.12316OpenAlexW4391177983MaRDI QIDQ6203153

Dmitry I. Sinelshchikov, Jaume Giné

Publication date: 27 February 2024

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2401.12316

zbMATH Keywords

Liénard equationstranscendental first integralsuperintegrable metrics

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37Jxx) Qualitative theory for ordinary differential equations (34Cxx) General theory for ordinary differential equations (34Axx)

Cites Work

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• Explicit metrics for a class of two-dimensional cubically superintegrable systems
• Rational integrals of the second degree of two-dimensional geodesic equations
• Integrability of dynamical systems: algebra and analysis
• Two-dimensional superintegrable metrics with one linear and one cubic integral
• Weierstrass integrability in Liénard differential systems
• Reduction of integrable planar polynomial differential systems
• On rational integrals of geodesic flows
• Invariant characterization of Liouville metrics and polynomial integrals
• Weierstrass integrability of differential equations
• Finite amplitude vibrations of a Mooney-Rivlin oscillator
• Superintegrable models on Riemannian surfaces of revolution with integrals of any integer degree. I
• Hypergeometric first integrals of the Duffing and van der Pol oscillators
• Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems
• Center problem with characteristic directions and inverse integrating factors
• Puiseux integrability of differential equations
• On linearizability via nonlocal transformations and first integrals for second-order ordinary differential equations
• Rational integrals of a natural mechanical system on the 2-torus
• Linearizability conditions for the Rayleigh-like oscillators
• Liouvillian integrability of the generalized Duffing oscillators
• Rational integrals of 2-dimensional geodesic flows: new examples
• Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity
• Metrisability of two-dimensional projective structures
• Localized pulsating solutions of the generalized complex cubic-quintic Ginzburg-Landau equation
• A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields
• Superintegrable Hamiltonian systems: Geometry and perturbations
• Qualitative theory of planar differential systems
• Lax representation and a quadratic rational first integral for second-order differential equations with cubic nonlinearity
• The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta
• Classical and quantum superintegrability with applications
• Liouvillian First Integrals of Differential Equations
• Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry
• Metrisability of Painlevé equations
• Open problems, questions and challenges in finite- dimensional integrable systems
• Superintegrability in a two-dimensional space of nonconstant curvature
• Open problems and questions about geodesics
• Strongly formal Weierstrass non-integrability for polynomial differential systems in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math>
• Symmetries and differential equations
• Linearizabiliy and Lax representations for cubic autonomous and non-autonomous nonlinear oscillators

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