Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System
A class of nonlinear Schrödinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov-Painlevé II equation which is linked, in turn, to the integrable Painlevé XXXIV equation. A nonlinear Schrödinger encapsu...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
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/123456789/148621 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System / C. Rogers, P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 92 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1486212019-02-19T01:26:12Z Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System Rogers, C. Clarkson, P.A. A class of nonlinear Schrödinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov-Painlevé II equation which is linked, in turn, to the integrable Painlevé XXXIV equation. A nonlinear Schrödinger encapsulation of a Korteweg-type capillary system is thereby used in the isolation of such a Ermakov-Painlevé II reduction valid for a multi-parameter class of free energy functions. Iterated application of a Bäcklund transformation then allows the construction of novel classes of exact solutions of the nonlinear capillarity system in terms of Yablonskii-Vorob'ev polynomials or classical Airy functions. A Painlevé XXXIV equation is derived for the density in the capillarity system and seen to correspond to the symmetry reduction of its Bernoulli integral of motion. 2017 Article Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System / C. Rogers, P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 92 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J15; 37K10; 76B45; 76D45 DOI:10.3842/SIGMA.2017.018 http://dspace.nbuv.gov.ua/handle/123456789/148621 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 |
A class of nonlinear Schrödinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov-Painlevé II equation which is linked, in turn, to the integrable Painlevé XXXIV equation. A nonlinear Schrödinger encapsulation of a Korteweg-type capillary system is thereby used in the isolation of such a Ermakov-Painlevé II reduction valid for a multi-parameter class of free energy functions. Iterated application of a Bäcklund transformation then allows the construction of novel classes of exact solutions of the nonlinear capillarity system in terms of Yablonskii-Vorob'ev polynomials or classical Airy functions. A Painlevé XXXIV equation is derived for the density in the capillarity system and seen to correspond to the symmetry reduction of its Bernoulli integral of motion. |
| format |
Article |
| author |
Rogers, C. Clarkson, P.A. |
| spellingShingle |
Rogers, C. Clarkson, P.A. Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Rogers, C. Clarkson, P.A. |
| author_sort |
Rogers, C. |
| title |
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System |
| title_short |
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System |
| title_full |
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System |
| title_fullStr |
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System |
| title_full_unstemmed |
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System |
| title_sort |
ermakov-painlevé ii symmetry reduction of a korteweg capillarity system |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148621 |
| citation_txt |
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System / C. Rogers, P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 92 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:30:15Z |
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2023-05-20T17:30:15Z |
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