New conservation forms and Lie algebras of Ermakov-Pinney equation
type: Item
instance of: scholarly article
title: New conservation forms and Lie algebras of Ermakov-Pinney equation
zbMATH Open document ID: 1385.22009
author: Özlem Orhan
author: Teoman Özer
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2018-01-19T00:00:00Z
review text: The authors discuss Noether symmetries of the nonlinear Ermakov-Pinney equation. Noether point symmetries and first integrals are presented. The generalized Prelle-Singer method is applied to the Ermakov-Pinney equation to obtain the first integrals and integrating factors. It is shown that the Hamiltonian and Lagrangian forms of the differential equations can be defined by using the method discussed in this article. For this purpose, the authors consider the first integrals and exact solutions of the Ermakov-Pinney equation by the approach related to the Prell-Singer and \(\lambda\)-symmetry. An extended bibliography is presented.
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 70B05
zbMATH DE Number: 6827652
zbMATH Keywords: Noether theory
zbMATH Keywords: first integral
zbMATH Keywords: classification
zbMATH Keywords: Prelle-Singer method
zbMATH Keywords: invariant solution
zbMATH Keywords: Lagrangian and Hamiltonian description
zbMATH Keywords: \(\lambda\)-symmetry
MaRDI profile type: Publication
full work available at URL: dcdss.2018046
OpenAlex ID: W2766313044
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DOI: 10.3934/DCDSS.2018046
description: scientific article; zbMATH DE number 6827652