Application of the λ-symmetries approach and time independent integral of the modified Emden equation

Detalhes bibliográficos
Autor(a) principal: Bhuvaneswari, A.
Data de Publicação: 2012
Outros Autores: Kraenkel, R. A., Senthilvelan, M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.nonrwa.2011.08.030
http://hdl.handle.net/11449/231278
Resumo: In this paper we derive the time-independent integral for a nonlinear dissipative system, namely the modified Emden equation, from Lie point symmetries. We employ the recently introduced λ-symmetries method [C. Muriel, J.L. Romero, First integrals, integrating factors and λ-symmetries of second-order differential equations, J. Phys. A: Math. Theor. 42 (2009) 365207365217] to complete this task. To begin with we recall Lie point symmetries of this system and derive λ-symmetries from the vector fields. The knowledge of λ-symmetries enables us to obtain integrating factors, integrals and the general solution for the linearizable case. While determining the integrating factor from the λ-symmetry for the integrable case we find that this case splits up into three sub-cases. We then obtain the integrating factor and integral for these three sub-cases. The results agree with the ones reported in the literature and thereby give a group theoretical interpretation for the nonstandard time independent integrals exhibited by the system. © 2011 Elsevier Ltd. All rights reserved.
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spelling Application of the λ-symmetries approach and time independent integral of the modified Emden equationλ-symmetriesIntegrabilityLie symmetriesIn this paper we derive the time-independent integral for a nonlinear dissipative system, namely the modified Emden equation, from Lie point symmetries. We employ the recently introduced λ-symmetries method [C. Muriel, J.L. Romero, First integrals, integrating factors and λ-symmetries of second-order differential equations, J. Phys. A: Math. Theor. 42 (2009) 365207365217] to complete this task. To begin with we recall Lie point symmetries of this system and derive λ-symmetries from the vector fields. The knowledge of λ-symmetries enables us to obtain integrating factors, integrals and the general solution for the linearizable case. While determining the integrating factor from the λ-symmetry for the integrable case we find that this case splits up into three sub-cases. We then obtain the integrating factor and integral for these three sub-cases. The results agree with the ones reported in the literature and thereby give a group theoretical interpretation for the nonstandard time independent integrals exhibited by the system. © 2011 Elsevier Ltd. All rights reserved.Centre for Nonlinear Dynamics Bharathidasan University, Tiruchirappalli 620024, Tamil NaduInstituto de Física Teórica, Rua Dr.Bento Teobaldo Ferraz 271, 01140-070, São PauloBharathidasan UniversityInstituto de Física TeóricaBhuvaneswari, A.Kraenkel, R. A.Senthilvelan, M.2022-04-29T08:44:28Z2022-04-29T08:44:28Z2012-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1102-1114http://dx.doi.org/10.1016/j.nonrwa.2011.08.030Nonlinear Analysis: Real World Applications, v. 13, n. 3, p. 1102-1114, 2012.1468-1218http://hdl.handle.net/11449/23127810.1016/j.nonrwa.2011.08.0302-s2.0-84655163138Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Analysis: Real World Applicationsinfo:eu-repo/semantics/openAccess2022-04-29T08:44:28Zoai:repositorio.unesp.br:11449/231278Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:33:32.320753Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Application of the λ-symmetries approach and time independent integral of the modified Emden equation
title Application of the λ-symmetries approach and time independent integral of the modified Emden equation
spellingShingle Application of the λ-symmetries approach and time independent integral of the modified Emden equation
Bhuvaneswari, A.
λ-symmetries
Integrability
Lie symmetries
title_short Application of the λ-symmetries approach and time independent integral of the modified Emden equation
title_full Application of the λ-symmetries approach and time independent integral of the modified Emden equation
title_fullStr Application of the λ-symmetries approach and time independent integral of the modified Emden equation
title_full_unstemmed Application of the λ-symmetries approach and time independent integral of the modified Emden equation
title_sort Application of the λ-symmetries approach and time independent integral of the modified Emden equation
author Bhuvaneswari, A.
author_facet Bhuvaneswari, A.
Kraenkel, R. A.
Senthilvelan, M.
author_role author
author2 Kraenkel, R. A.
Senthilvelan, M.
author2_role author
author
dc.contributor.none.fl_str_mv Bharathidasan University
Instituto de Física Teórica
dc.contributor.author.fl_str_mv Bhuvaneswari, A.
Kraenkel, R. A.
Senthilvelan, M.
dc.subject.por.fl_str_mv λ-symmetries
Integrability
Lie symmetries
topic λ-symmetries
Integrability
Lie symmetries
description In this paper we derive the time-independent integral for a nonlinear dissipative system, namely the modified Emden equation, from Lie point symmetries. We employ the recently introduced λ-symmetries method [C. Muriel, J.L. Romero, First integrals, integrating factors and λ-symmetries of second-order differential equations, J. Phys. A: Math. Theor. 42 (2009) 365207365217] to complete this task. To begin with we recall Lie point symmetries of this system and derive λ-symmetries from the vector fields. The knowledge of λ-symmetries enables us to obtain integrating factors, integrals and the general solution for the linearizable case. While determining the integrating factor from the λ-symmetry for the integrable case we find that this case splits up into three sub-cases. We then obtain the integrating factor and integral for these three sub-cases. The results agree with the ones reported in the literature and thereby give a group theoretical interpretation for the nonstandard time independent integrals exhibited by the system. © 2011 Elsevier Ltd. All rights reserved.
publishDate 2012
dc.date.none.fl_str_mv 2012-06-01
2022-04-29T08:44:28Z
2022-04-29T08:44:28Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.nonrwa.2011.08.030
Nonlinear Analysis: Real World Applications, v. 13, n. 3, p. 1102-1114, 2012.
1468-1218
http://hdl.handle.net/11449/231278
10.1016/j.nonrwa.2011.08.030
2-s2.0-84655163138
url http://dx.doi.org/10.1016/j.nonrwa.2011.08.030
http://hdl.handle.net/11449/231278
identifier_str_mv Nonlinear Analysis: Real World Applications, v. 13, n. 3, p. 1102-1114, 2012.
1468-1218
10.1016/j.nonrwa.2011.08.030
2-s2.0-84655163138
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Analysis: Real World Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1102-1114
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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