Ordinary differential equations invariant under translation in the independent variable and rescaling: The Lagrangian formulation

DOI10.1016/j.jmaa.2004.10.005zbMath1088.34033OpenAlexW2017039690MaRDI QIDQ1779338

S. Moyo, Peter G. L. Leach

Publication date: 1 June 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.10.005

zbMATH Keywords

self-similarityrescalingLagrangiansecond-order ordinary differential equationsPainlevé analysis

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Hamiltonian and Lagrangian mechanics (70H99)

Cites Work

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• Symmetry Lie algebras of \(n\)th order ordinary differential equations
• Properties of second-order ordinary differential equations invariant under time translation and self-similar transformation
• Integrability analysis of the Emden-Fowler equation
• First integrals for the modified Emden equation q̈+α(t) q̇+q n =0
• THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
• A class of second-order differential equations and related first-order systems
• On the singularity analysis of ordinary differential equations invariant under time translation and rescaling
• Analysis and solution of a nonlinear second-order differential equation through rescaling and through a dynamical point of view
• The Painleve test, hidden symmetries and the equation y"+yy'+Ky³=0
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0

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