Properties of second-order ordinary differential equations invariant under time translation and self-similar transformation

DOI10.1063/1.529306zbMath0734.34029OpenAlexW2047408525MaRDI QIDQ3361162

Marc R. Feix, S. Bouquet, Peter G. L. Leach

Publication date: 1991

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529306

zbMATH Keywords

asymptotic behaviorlimit cycleperiodsecond-order ordinary differential equationphysical interpretationtime translationself- similarity

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear ordinary differential equations and systems (34A34) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items

Symmetry and singularity properties of second-order ordinary differential equations of Lie's Type III., Autonomous self-similar ordinary differential equations and the Painlevé connection, Hamiltonian structure and integrability of the stationary Kuramoto–Sivashinsky equation, Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II, Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit, Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator, First Integrals and Parametric Solutions for Equations Integrable Through Lie Symmetries, On the local analytic integrability for a generalized damped nonlinear oscillator equation, Ordinary differential equations invariant under translation in the independent variable and rescaling: The Lagrangian formulation, Generalisations of the LaplaceRungeLenz Vector

Cites Work

• Invariants for time-dependent potentials: Use of self-similar techniques
• Symmetries of nonlinear differential equations and linearisation
• Invariants for dissipative nonlinear systems by using rescaling
• First integrals for the modified Emden equation q̈+α(t) q̇+q n =0
• THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
• An exact invariant for a class of time-dependent anharmonic oscillators with cubic anharmonicity
• Analysis and solution of a nonlinear second-order differential equation through rescaling and through a dynamical point of view
• THE LIE ALGEBRA sl(3, R) AND LINEARIZATION
• Lie algebras associated with scalar second-order ordinary differential equations