Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://repositorio.inesctec.pt/handle/123456789/6218 http://dx.doi.org/10.1103/physreve.92.022922 |
Resumo: | We found two stationary solutions of the cubic complex Ginzburg-Landau equation (CGLE) with an additional term modeling the delayed Raman scattering. Both solutions propagate with nonzero velocity. The solution that has lower peak amplitude is the continuation of the chirped soliton of the cubic CGLE and is unstable in all the parameter space of existence. The other solution is stable for values of nonlinear gain below a certain threshold. The solutions were found using a shooting method to integrate the ordinary differential equation that results from the evolution equation through a change of variables, and their stability was studied using the Evans function method. Additional integration of the evolution equation revealed the basis of attraction of the stable solutions. Furthermore, we have investigated the existence and stability of the high amplitude branch of solutions in the presence of other higher order terms originating from complex Raman, self-steepening, and imaginary group velocity. |
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Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scatteringWe found two stationary solutions of the cubic complex Ginzburg-Landau equation (CGLE) with an additional term modeling the delayed Raman scattering. Both solutions propagate with nonzero velocity. The solution that has lower peak amplitude is the continuation of the chirped soliton of the cubic CGLE and is unstable in all the parameter space of existence. The other solution is stable for values of nonlinear gain below a certain threshold. The solutions were found using a shooting method to integrate the ordinary differential equation that results from the evolution equation through a change of variables, and their stability was studied using the Evans function method. Additional integration of the evolution equation revealed the basis of attraction of the stable solutions. Furthermore, we have investigated the existence and stability of the high amplitude branch of solutions in the presence of other higher order terms originating from complex Raman, self-steepening, and imaginary group velocity.2018-01-15T18:36:29Z2015-01-01T00:00:00Z2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://repositorio.inesctec.pt/handle/123456789/6218http://dx.doi.org/10.1103/physreve.92.022922engFacao,MMaria Inês Carvalhoinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-05-15T10:20:23Zoai:repositorio.inesctec.pt:123456789/6218Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:53:02.904157Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering |
title |
Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering |
spellingShingle |
Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering Facao,M |
title_short |
Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering |
title_full |
Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering |
title_fullStr |
Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering |
title_full_unstemmed |
Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering |
title_sort |
Existence and stability of solutions of the cubic complex Ginzburg-Landau equation with delayed Raman scattering |
author |
Facao,M |
author_facet |
Facao,M Maria Inês Carvalho |
author_role |
author |
author2 |
Maria Inês Carvalho |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Facao,M Maria Inês Carvalho |
description |
We found two stationary solutions of the cubic complex Ginzburg-Landau equation (CGLE) with an additional term modeling the delayed Raman scattering. Both solutions propagate with nonzero velocity. The solution that has lower peak amplitude is the continuation of the chirped soliton of the cubic CGLE and is unstable in all the parameter space of existence. The other solution is stable for values of nonlinear gain below a certain threshold. The solutions were found using a shooting method to integrate the ordinary differential equation that results from the evolution equation through a change of variables, and their stability was studied using the Evans function method. Additional integration of the evolution equation revealed the basis of attraction of the stable solutions. Furthermore, we have investigated the existence and stability of the high amplitude branch of solutions in the presence of other higher order terms originating from complex Raman, self-steepening, and imaginary group velocity. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-01-01T00:00:00Z 2015 2018-01-15T18:36:29Z |
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://repositorio.inesctec.pt/handle/123456789/6218 http://dx.doi.org/10.1103/physreve.92.022922 |
url |
http://repositorio.inesctec.pt/handle/123456789/6218 http://dx.doi.org/10.1103/physreve.92.022922 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799131605497806849 |