On uniqueness and decay of solution to the Hirota equation
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/16888 |
Resumo: | We address the question of the uniqueness of solution to the initial value problem associated to the equation \begin{equation*} \partial_{t}u+i\alpha \partial^{2}_{x}u+\beta \partial^{3}_{x}u+i\gamma|u|^{2}u+\delta |u|^{2}\partial_{x}u+\epsilon u^{2}\partial_{x}\overline{u} = 0, \quad x,t \in \mathbb{R}, \end{equation*} and prove that a certain decay property of the difference $u_1-u_2$ of two solutions $u_1$ and $u_2$ at two different instants of times $t=0$ and $t=1$, is sufficient to ensure that $u_1=u_2$ for all the time. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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On uniqueness and decay of solution to the Hirota equationSchr\"{o}dinger equationKorteweg-de vries equationSmooth solutionCompact supportUnique continuation propertySchrödinger equationScience & TechnologyWe address the question of the uniqueness of solution to the initial value problem associated to the equation \begin{equation*} \partial_{t}u+i\alpha \partial^{2}_{x}u+\beta \partial^{3}_{x}u+i\gamma|u|^{2}u+\delta |u|^{2}\partial_{x}u+\epsilon u^{2}\partial_{x}\overline{u} = 0, \quad x,t \in \mathbb{R}, \end{equation*} and prove that a certain decay property of the difference $u_1-u_2$ of two solutions $u_1$ and $u_2$ at two different instants of times $t=0$ and $t=1$, is sufficient to ensure that $u_1=u_2$ for all the time.FCTElsevierUniversidade do MinhoCarvajal, XavierPanthee, Mahendra Prasad20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/16888eng0096-300310.1016/j.amc.2011.10.058info: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:RCAAP2023-07-21T12:48:34Zoai:repositorium.sdum.uminho.pt:1822/16888Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:46:51.136671Repositório 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 |
On uniqueness and decay of solution to the Hirota equation |
title |
On uniqueness and decay of solution to the Hirota equation |
spellingShingle |
On uniqueness and decay of solution to the Hirota equation Carvajal, Xavier Schr\"{o}dinger equation Korteweg-de vries equation Smooth solution Compact support Unique continuation property Schrödinger equation Science & Technology |
title_short |
On uniqueness and decay of solution to the Hirota equation |
title_full |
On uniqueness and decay of solution to the Hirota equation |
title_fullStr |
On uniqueness and decay of solution to the Hirota equation |
title_full_unstemmed |
On uniqueness and decay of solution to the Hirota equation |
title_sort |
On uniqueness and decay of solution to the Hirota equation |
author |
Carvajal, Xavier |
author_facet |
Carvajal, Xavier Panthee, Mahendra Prasad |
author_role |
author |
author2 |
Panthee, Mahendra Prasad |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Carvajal, Xavier Panthee, Mahendra Prasad |
dc.subject.por.fl_str_mv |
Schr\"{o}dinger equation Korteweg-de vries equation Smooth solution Compact support Unique continuation property Schrödinger equation Science & Technology |
topic |
Schr\"{o}dinger equation Korteweg-de vries equation Smooth solution Compact support Unique continuation property Schrödinger equation Science & Technology |
description |
We address the question of the uniqueness of solution to the initial value problem associated to the equation \begin{equation*} \partial_{t}u+i\alpha \partial^{2}_{x}u+\beta \partial^{3}_{x}u+i\gamma|u|^{2}u+\delta |u|^{2}\partial_{x}u+\epsilon u^{2}\partial_{x}\overline{u} = 0, \quad x,t \in \mathbb{R}, \end{equation*} and prove that a certain decay property of the difference $u_1-u_2$ of two solutions $u_1$ and $u_2$ at two different instants of times $t=0$ and $t=1$, is sufficient to ensure that $u_1=u_2$ for all the time. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012 2012-01-01T00:00:00Z |
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://hdl.handle.net/1822/16888 |
url |
http://hdl.handle.net/1822/16888 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0096-3003 10.1016/j.amc.2011.10.058 |
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.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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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1799133039767322624 |