Application of the λ-symmetries approach and time independent integral of the modified Emden equation
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | , |
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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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 |
|
_version_ |
1808128530962186240 |