Skip to main content

Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System

Rogers, Colin and Clarkson, Peter (2017) Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System. Technical report. arXiv.org

PDF - Pre-print
Download (240kB) Preview
[img]
Preview
Official URL
https://arxiv.org/abs/1701.03238

Abstract

A class of nonlinear Schr\"{o}dinger 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-Painlev\'{e} II equation which is linked, in turn, to the integrable Painlev\'{e} XXXIV equation. A nonlinear Schr\"{o}dinger encapsulation of a Korteweg-type capillary system is thereby used in the isolation of such a Ermakov-Painlev\'{e} II reduction valid for a multi-parameter class of free energy functions. Iterated application of a B\"{a}cklund 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 Painlev\'{e} 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: Monograph (Technical report)
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter A Clarkson
Date Deposited: 18 Jan 2017 06:35 UTC
Last Modified: 29 May 2019 18:33 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/59909 (The current URI for this page, for reference purposes)
Clarkson, Peter: https://orcid.org/0000-0002-8777-5284
  • Depositors only (login required):

Downloads

Downloads per month over past year