Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries
The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above...
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| Дата: | 2017 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148631 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries / S.Y. Startsev // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 38 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1486312019-02-19T01:31:43Z Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries Startsev, S.Y. The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator. 2017 Article Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries / S.Y. Startsev // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 38 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K05; 37K10; 37K35; 35L65; 35L70 DOI:10.3842/SIGMA.2017.034 http://dspace.nbuv.gov.ua/handle/123456789/148631 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 |
The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator. |
| format |
Article |
| author |
Startsev, S.Y. |
| spellingShingle |
Startsev, S.Y. Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Startsev, S.Y. |
| author_sort |
Startsev, S.Y. |
| title |
Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries |
| title_short |
Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries |
| title_full |
Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries |
| title_fullStr |
Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries |
| title_full_unstemmed |
Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries |
| title_sort |
formal integrals and noether operators of nonlinear hyperbolic partial differential systems admitting a rich set of symmetries |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148631 |
| citation_txt |
Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries / S.Y. Startsev // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 38 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:30:54Z |
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2023-05-20T17:30:54Z |
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