Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System
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| Creator |
Rogers, C.
Clarkson, P.A. |
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| 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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| Date |
2019-02-18T16:43:33Z
2019-02-18T16:43:33Z 2017 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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