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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2017, том 13, 018, 20 стр. (Mi sigma1218)

Эта публикация цитируется в 8 статьях

Ermakov–Painlevé II Symmetry Reduction of a Korteweg Capillarity System

Colin Rogersab, Peter A. Clarksonc

a Australian Research Council Centre of Excellence for Mathematics & Statistics of Complex Systems
b School of Mathematics, The University of New South Wales, Sydney, NSW2052, Australia
c School of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, CT2 7FS, UK

Аннотация: 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.

Ключевые слова: Ermakov–Painlevé II equation; Painlevé capillarity; Korteweg-type capillary system; Bäcklund transformation.

MSC: 37J15; 37K10; 76B45; 76D45

Поступила: 13 января 2017 г.; в окончательном варианте 15 марта 2017 г.; опубликована 22 марта 2017 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2017.018



Реферативные базы данных:
ArXiv: 1701.03238


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