Transformations of quadrilateral lattices

Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogs: the multidimensional quadrilateral lattices, i.e., lattices x:Z(N)--> R-M, N less than or equal to M, whose elementary quadrilaterals are...

Descripción completa

Detalles Bibliográficos
Autores: Doliwa, Adam, Santin, Maria Santin, Mañas Baena, Manuel Enrique
Tipo de recurso: artículo
Fecha de publicación:2000
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/59689
Acceso en línea:https://hdl.handle.net/20.500.14352/59689
Access Level:acceso abierto
Palabra clave:51-73
Integrable hierarchies
Coordinate systems
Hydrodynamic-type
Equation
Surfaces
Discretization
Física-Modelos matemáticos
Física matemática
id ES_a76bf25a6afa8de36ba59bcc0b2fa8c7
oai_identifier_str oai:docta.ucm.es:20.500.14352/59689
network_acronym_str ES
network_name_str España
repository_id_str
spelling Transformations of quadrilateral latticesDoliwa, AdamSantin, Maria SantinMañas Baena, Manuel Enrique51-73Integrable hierarchiesCoordinate systemsHydrodynamic-typeEquationSurfacesDiscretizationFísica-Modelos matemáticosFísica matemáticaMotivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogs: the multidimensional quadrilateral lattices, i.e., lattices x:Z(N)--> R-M, N less than or equal to M, whose elementary quadrilaterals are planar. Our investigation is based on the discrete analog of the theory of the rectilinear congruences, which we also present in detail. We study, in particular, the discrete analogs of the Laplace, Combescure, Levy, radial, and fundamental transformations and their interrelations. The composition of these transformations and their permutability is also investigated from a geometric point of view. The deep connections between "transformations" and "discretizations" is also investigated for quadrilateral lattices. We finally interpret these results within the <(partial derivative)over bar> formalism.American Institute of PhysicsUniversidad Complutense de Madrid20002000-02-0120002000-02-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/59689reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/596892026-06-02T12:44:21Z
dc.title.none.fl_str_mv Transformations of quadrilateral lattices
title Transformations of quadrilateral lattices
spellingShingle Transformations of quadrilateral lattices
Doliwa, Adam
51-73
Integrable hierarchies
Coordinate systems
Hydrodynamic-type
Equation
Surfaces
Discretization
Física-Modelos matemáticos
Física matemática
title_short Transformations of quadrilateral lattices
title_full Transformations of quadrilateral lattices
title_fullStr Transformations of quadrilateral lattices
title_full_unstemmed Transformations of quadrilateral lattices
title_sort Transformations of quadrilateral lattices
dc.creator.none.fl_str_mv Doliwa, Adam
Santin, Maria Santin
Mañas Baena, Manuel Enrique
author Doliwa, Adam
author_facet Doliwa, Adam
Santin, Maria Santin
Mañas Baena, Manuel Enrique
author_role author
author2 Santin, Maria Santin
Mañas Baena, Manuel Enrique
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-73
Integrable hierarchies
Coordinate systems
Hydrodynamic-type
Equation
Surfaces
Discretization
Física-Modelos matemáticos
Física matemática
topic 51-73
Integrable hierarchies
Coordinate systems
Hydrodynamic-type
Equation
Surfaces
Discretization
Física-Modelos matemáticos
Física matemática
description Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogs: the multidimensional quadrilateral lattices, i.e., lattices x:Z(N)--> R-M, N less than or equal to M, whose elementary quadrilaterals are planar. Our investigation is based on the discrete analog of the theory of the rectilinear congruences, which we also present in detail. We study, in particular, the discrete analogs of the Laplace, Combescure, Levy, radial, and fundamental transformations and their interrelations. The composition of these transformations and their permutability is also investigated from a geometric point of view. The deep connections between "transformations" and "discretizations" is also investigated for quadrilateral lattices. We finally interpret these results within the <(partial derivative)over bar> formalism.
publishDate 2000
dc.date.none.fl_str_mv 2000
2000-02-01
2000
2000-02-01
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/20.500.14352/59689
url https://hdl.handle.net/20.500.14352/59689
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
_version_ 1869415776973225984
score 15.301603

Similares en LA Referencia