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Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System

Rogers, Colin, Clarkson, Peter (2017) Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System. Symmetry, Integrability and Geometry: Methods and Applications, 13 (18). ISSN 1815-0659. (doi:10.3842/SIGMA.2017.018)

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https://doi.org/10.3842/SIGMA.2017.018

Abstract

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

Item Type: Article
DOI/Identification number: 10.3842/SIGMA.2017.018
Uncontrolled keywords: Ermakov-Painlevé II equation; Painlevé capillarity; Korteweg-type capillary system; Bäcklund transformation.
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter A Clarkson
Date Deposited: 08 May 2017 15:22 UTC
Last Modified: 29 May 2019 19:02 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/61649 (The current URI for this page, for reference purposes)
Clarkson, Peter: https://orcid.org/0000-0002-8777-5284
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