248 research outputs found
Group Classification of a family of second-order differential equations
We find the group of equivalence transformations for equations of the form
where and 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
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
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
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
Lie symmetries and criticality of semilinear differential systems
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. L3FAPESP - 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)[INTAS-05-100000B-792]SEM INFORMAÇÃOSEM INFORMAÇÃ
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
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