Contact Geometry of Hyperbolic Equations of Generic Type
We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6), Goursat (class 6-7) and generic (class 7-7) hyperbolic equations, we use Cartan's equivalenc...
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| Дата: | 2008 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149023 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Contact Geometry of Hyperbolic Equations of Generic Type / D. The // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 26 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1490232019-02-21T01:24:01Z Contact Geometry of Hyperbolic Equations of Generic Type The, D. We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6), Goursat (class 6-7) and generic (class 7-7) hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit symmetry algebras are presented. Moreover, these maximally symmetric equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional) generic hyperbolic structures is also given. 2008 Article Contact Geometry of Hyperbolic Equations of Generic Type / D. The // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 26 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35A30; 35L70; 58J70 http://dspace.nbuv.gov.ua/handle/123456789/149023 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6), Goursat (class 6-7) and generic (class 7-7) hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit symmetry algebras are presented. Moreover, these maximally symmetric equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional) generic hyperbolic structures is also given. |
| format |
Article |
| author |
The, D. |
| spellingShingle |
The, D. Contact Geometry of Hyperbolic Equations of Generic Type Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
The, D. |
| author_sort |
The, D. |
| title |
Contact Geometry of Hyperbolic Equations of Generic Type |
| title_short |
Contact Geometry of Hyperbolic Equations of Generic Type |
| title_full |
Contact Geometry of Hyperbolic Equations of Generic Type |
| title_fullStr |
Contact Geometry of Hyperbolic Equations of Generic Type |
| title_full_unstemmed |
Contact Geometry of Hyperbolic Equations of Generic Type |
| title_sort |
contact geometry of hyperbolic equations of generic type |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149023 |
| citation_txt |
Contact Geometry of Hyperbolic Equations of Generic Type / D. The // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 26 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT thed contactgeometryofhyperbolicequationsofgenerictype |
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2023-05-20T17:32:00Z |
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2023-05-20T17:32:00Z |
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1796153500603777024 |