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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148621 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862549114489667584 |
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| author | Rogers, C. Clarkson, P.A. |
| author_facet | Rogers, C. Clarkson, P.A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-25T20:31:26Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148621 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T20:31:26Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rogers, C. Clarkson, P.A. 2019-02-18T16:43:33Z 2019-02-18T16:43:33Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148621 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System Article published earlier |
| spellingShingle | Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System Rogers, C. Clarkson, P.A. |
| title | 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_short | Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System |
| title_sort | ermakov-painlevé ii symmetry reduction of a korteweg capillarity system |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148621 |
| work_keys_str_mv | AT rogersc ermakovpainleveiisymmetryreductionofakortewegcapillaritysystem AT clarksonpa ermakovpainleveiisymmetryreductionofakortewegcapillaritysystem |