Invariant differential equations and the Adler-Gel'fand-Dikii bracket

In this paper we find an explicit formula for the most general vector evolution of curves on RPn−1 invariant under the projective action of SL(n, R). When this formula is applied to the projectivization of solution curves of scalar Lax operators with periodic coefficients, one obtains a correspondin...

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Detalles Bibliográficos
Autores: González López, Artemio, Hernández Heredero, Rafael, Beffa, Gloria Marí
Tipo de recurso: artículo
Fecha de publicación:1997
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/59725
Acceso en línea:https://hdl.handle.net/20.500.14352/59725
Access Level:acceso abierto
Palabra clave:51-73
Korteweg-devries type
Física-Modelos matemáticos
Física matemática
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spelling Invariant differential equations and the Adler-Gel'fand-Dikii bracketGonzález López, ArtemioHernández Heredero, RafaelBeffa, Gloria Marí51-73Korteweg-devries typeFísica-Modelos matemáticosFísica matemáticaIn this paper we find an explicit formula for the most general vector evolution of curves on RPn−1 invariant under the projective action of SL(n, R). When this formula is applied to the projectivization of solution curves of scalar Lax operators with periodic coefficients, one obtains a corresponding evolution in the space of such operators. We conjecture that this evolution is identical to the second KdV Hamiltonian evolution under appropriate conditions. These conditions give a Hamiltonian interpretation of general vector differential invariants for the projective action of SL(n, R), namely, the SL(n, R) invariant evolution can be written so that a general vector differential invariant corresponds to the Hamiltonian pseudo-differential operator. We find common coordinates and simplify both evolutions so that one can attempt to prove the equivalence for arbitrary n .American Institute of PhysicsUniversidad Complutense de Madrid19971997-11-0119971997-11-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/59725reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/597252026-06-02T12:44:21Z
dc.title.none.fl_str_mv Invariant differential equations and the Adler-Gel'fand-Dikii bracket
title Invariant differential equations and the Adler-Gel'fand-Dikii bracket
spellingShingle Invariant differential equations and the Adler-Gel'fand-Dikii bracket
González López, Artemio
51-73
Korteweg-devries type
Física-Modelos matemáticos
Física matemática
title_short Invariant differential equations and the Adler-Gel'fand-Dikii bracket
title_full Invariant differential equations and the Adler-Gel'fand-Dikii bracket
title_fullStr Invariant differential equations and the Adler-Gel'fand-Dikii bracket
title_full_unstemmed Invariant differential equations and the Adler-Gel'fand-Dikii bracket
title_sort Invariant differential equations and the Adler-Gel'fand-Dikii bracket
dc.creator.none.fl_str_mv González López, Artemio
Hernández Heredero, Rafael
Beffa, Gloria Marí
author González López, Artemio
author_facet González López, Artemio
Hernández Heredero, Rafael
Beffa, Gloria Marí
author_role author
author2 Hernández Heredero, Rafael
Beffa, Gloria Marí
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-73
Korteweg-devries type
Física-Modelos matemáticos
Física matemática
topic 51-73
Korteweg-devries type
Física-Modelos matemáticos
Física matemática
description In this paper we find an explicit formula for the most general vector evolution of curves on RPn−1 invariant under the projective action of SL(n, R). When this formula is applied to the projectivization of solution curves of scalar Lax operators with periodic coefficients, one obtains a corresponding evolution in the space of such operators. We conjecture that this evolution is identical to the second KdV Hamiltonian evolution under appropriate conditions. These conditions give a Hamiltonian interpretation of general vector differential invariants for the projective action of SL(n, R), namely, the SL(n, R) invariant evolution can be written so that a general vector differential invariant corresponds to the Hamiltonian pseudo-differential operator. We find common coordinates and simplify both evolutions so that one can attempt to prove the equivalence for arbitrary n .
publishDate 1997
dc.date.none.fl_str_mv 1997
1997-11-01
1997
1997-11-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/59725
url https://hdl.handle.net/20.500.14352/59725
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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