On Symbolic Solutions of Algebraic Partial Differential Equations

Authors
Grasegger, Georg; Sendra Pons, Juan RafaelUniversity of Alcalá Author; Lastra Sedano, AlbertoUniversity of Alcalá Author; Winkler, FranzUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20704
DOI: 10.1007/978-3-319-10515-4_9
ISBN: 978-3-319-10514-7
Publisher
Springer
Date
2014
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Ciencia e Innovación
Ministerio de Economía y Competitividad
Bibliographic citation
Proc.CAS., 2014, p. 111-120
Keywords
Partial di erential equations
Partial differential equations
Algebraic surfaces
Rational parametrizations
Radical Parametrizations
Description / Notes
The final version of this paper appears in Grasegger G., Lastra A., Sendra J.R. and Winkler F. (2014). On symbolic solutions of algebraic partial differential equations, Proc. CASC 2014 SpringerVerlag LNCS 8660 pp. 111-120. DOI 10.1007/978-3-319-10515-4_9 and it is available at at Springer via http://DOI 10.1007/978-3-319-10515-4_9
Project
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
info:eu-repo/grantAgreement/MINECO//MTM2012-31439/ES/ANALISIS DE PERTURBACIONES SINGULARES: ESTUDIO ASINTOTICO, CAPAS LIMITE Y FENOMENOS MULTIESCALA/
Document type
info:eu-repo/semantics/conferenceObject
Version
info:eu-repo/semantics/submittedVersion
Publisher's version
http://dx.doi.org/10.1007/978-3-319-10515-4_9
Rights
© Springer International Publishing Switzerland, 2014
Access rights
info:eu-repo/semantics/openAccess
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Abstract
In this paper we present a general procedure for solving rst-order autonomous algebraic partial di erential equations in two independent variables. The method uses proper rational parametrizations of algebraic surfaces and generalizes a similar procedure for rst-order autonomous ordinary di erential equations. We will demonstrate in examples that, depending on certain steps in the procedure, rational, radical or even non-algebraic solutions can be found. Solutions computed by the procedure will depend on two arbitrary independent constants.
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