The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas
To every Darboux integrable system there is an associated Lie group G which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149223 |
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| Zitieren: | The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas / I.M. Anderson, M.E. Fels // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 16 назв. — англ. |
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Anderson, I.M. Fels, M.E. 2019-02-19T19:00:11Z 2019-02-19T19:00:11Z 2013 The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas / I.M. Anderson, M.E. Fels // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58A15; 35L52; 58J70; 35A30; 34A26 DOI: http://dx.doi.org/10.3842/SIGMA.2013.017 https://nasplib.isofts.kiev.ua/handle/123456789/149223 To every Darboux integrable system there is an associated Lie group G which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the Vessiot group G. If the Vessiot group G is solvable then the Cauchy problem can be solved by quadratures. This allows us to give explicit integral formulas, similar to the well known d'Alembert's formula for the wave equation, to the initial value problem with generic non-characteristic initial data. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas |
| spellingShingle |
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas Anderson, I.M. Fels, M.E. |
| title_short |
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas |
| title_full |
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas |
| title_fullStr |
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas |
| title_full_unstemmed |
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas |
| title_sort |
cauchy problem for darboux integrable systems and non-linear d'alembert formulas |
| author |
Anderson, I.M. Fels, M.E. |
| author_facet |
Anderson, I.M. Fels, M.E. |
| publishDate |
2013 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
To every Darboux integrable system there is an associated Lie group G which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the Vessiot group G. If the Vessiot group G is solvable then the Cauchy problem can be solved by quadratures. This allows us to give explicit integral formulas, similar to the well known d'Alembert's formula for the wave equation, to the initial value problem with generic non-characteristic initial data.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149223 |
| citation_txt |
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas / I.M. Anderson, M.E. Fels // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 16 назв. — англ. |
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