First Integrals and Parametric Solutions for Equations Integrable Through Lie Symmetries

DOI10.2991/jnmp.2001.8.2.4zbMath0988.34028arXivnlin/0104074OpenAlexW3099042542MaRDI QIDQ2747840

Marc R. Feix, Claude Géronimi, Peter G. L. Leach

Publication date: 26 June 2002

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

Full work available at URL: https://arxiv.org/abs/nlin/0104074

zbMATH Keywords

integrable equationsparametric solutions

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Explicit solutions, first integrals of ordinary differential equations (34A05)

Cites Work

• Characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry
• Properties of second-order ordinary differential equations invariant under time translation and self-similar transformation
• 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

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