Nonlinear ordinary differential equations: A discussion on symmetries and singularities

DOI10.1142/S0219887816300099zbMath1387.34049arXiv1605.04164WikidataQ115245381 ScholiaQ115245381MaRDI QIDQ2816546

Andronikos Paliathanasis, Peter G. L. Leach

Publication date: 23 August 2016

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.04164

zbMATH Keywords

integrabilityLie symmetriessingularity analysis

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Related Items (13)

Lie symmetries and singularity analysis for generalized shallow-water equations ⋮ Lie symmetry analysis and similarity solutions for the Jimbo-Miwa equation and generalisations ⋮ Symmetries and singularities of the Szekeres system ⋮ Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations ⋮ One-dimensional optimal system and similarity transformations for the \(3+1\) Kudryashov-Sinelshchikov equation ⋮ Singularity analysis and analytic solutions for the Benney-Gjevik equations ⋮ Nonlocal representation of the sl(2, R) algebra for the Chazy equation ⋮ A systematic analysis of the properties of the generalised Painlevé-Ince equation ⋮ Unnamed Item ⋮ Singularity analysis of a variant of the Painlevé-Ince equation ⋮ Noether's theorem and symmetry ⋮ Exact solutions, finite time singularities and non-singular universe models from a variety of Λ(t) cosmologies ⋮ Approximate symmetries and similarity solutions for wave equations on liquid films

Uses Software

• REDUCE
• DIMSYM
• SYM
• LIE

Cites Work

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• On the systematic approach to the classification of differential equations by group theoretical methods
• Integration of some nonlinear systems of ordinary differential equations
• Characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry
• Equations différentielles du second ordre en Y et du second degré en Y dont l'intégrale générale est à points critiques fixes
• Symmetry, singularities, and integrability in complex dynamics. II: Rescaling and time-translation in two-dimensional systems
• The Painlevé property. One century later
• Differential equations with fixed critical points. II
• Differential equations with fixed critical points
• Symmetry, Singularities and Integrability in Complex Dynamics III: Approximate Symmetries and Invariants
• Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1
• A note on the invariants for the time-dependent oscillator
• THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
• A class of second-order differential equations and related first-order systems
• Lie point symmetries for systems of second order linear ordinary differential equations
• A group theoretic approach to a class of second-order ordinary differential equations not possessing Lie point symmetries
• The algebraic structure of generalized Ermakov systems in three dimensions
• The Painleve test, hidden symmetries and the equation y"+yy'+Ky³=0
• On the complete symmetry group of the classical Kepler system
• Chazy Classes IX–XI Of Third‐Order Differential Equations
• Symmetries and Integrating Factors
• LIE, a PC program for Lie analysis of differential equations
• Complete symmetry groups of ordinary differential equations and their integrals: Some basic considerations

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