Group Classification of a family of second-order differential equations

We find the group of equivalence transformations for equations of the form $y''= A(x)y' + F(y),$ where $A$ and $F$ are arbitrary functions. We then give a complete group classification of these families of equations, using a direct method of analysis, together with the equivalence transformations.Comment: 13 page

Noether Symmetries and Critical Exponents

We show that all Lie point symmetries of various classes of nonlinear differential equations involving critical nonlinearities are variational/divergence symmetries.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Symmetry analysis of the bidimensional Lane-Emden systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We carry out a complete group classification of the nonlinear Lane-Emden systems; in dimension two. The Noether symmetries are found and their corresponding conservation laws are established. (C) 2011 Elsevier Inc. All rights reserved.We carry out a complete group classification of the nonlinear Lane-Emden systems; in dimension two. The Noether symmetries are found and their corresponding conservation laws are established388212791284FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)SEM INFORMAÇÃOSEM INFORMAÇÃ

Remarks on symmetry analysis of Lane-Emden systems of dimensions one and two

Some recent results on Lie group analysis of the one and bi-dimensional Lane-Emden systems are revisited.Alguns resultados recentes sobre simetrias de Lie de sistemas de Lane-Emden uni e bidimensionais são revisitados.245254Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Generating Finite Dimensional Integrable Nonlinear Dynamical Systems

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties, including quantum aspects. Particularly we concentrate on Lienard type nonlinear oscillators and their generalizations and coupled versions. Specific systems include Mathews-Lakshmanan oscillators, modified Emden equations, isochronous oscillators and generalizations. Nonstandard Lagrangian and Hamiltonian formulations of some of these systems are also briefly touched upon. Nonlocal transformations and linearization aspects are also discussed.Comment: To appear in Eur. Phys. J - ST 222, 665 (2013

Group Analysis of Nonlinear Fin Equations

Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of truly nonlinear equations for the class under consideration. Nonclassical symmetries of the fin equations are discussed. Adduced results amend and essentially generalize recent works on the subject [M. Pakdemirli and A.Z. Sahin, Appl. Math. Lett., 2006, V.19, 378-384; A.H. Bokhari, A.H. Kara and F.D. Zaman, Appl. Math. Lett., 2006, V.19, 1356-1340].Comment: 6 page

Risultati tipo Liouville per l'equazione di Lane-Emden

We present some Liouville-type result for the Lane-Emden equation in the subcritical and in the critical regimes. In particular, we focus on the so-called critical p-Laplace equation.Presentiamo alcuni risultati di tipo Liouville per l'equazione di Lane-Emded nei casi sottocritico e critico. In particolare, ci concentriamo sull'equazione critica del p-Laplaciano