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On a Painlevé II model in steady electrolysis: application of a Bäcklund transformation

journal contribution
posted on 2023-05-18, 19:07 authored by Rogers, C, Andrew BassomAndrew Bassom, Schief, WK
A model equation of Painlevé II type was introduced by Bass in 1964 in connection with a boundary value problem which describes the electric field distribution in a region x > 0 occupied by an electrolyte. This is possibly the earliest explicit physical application of a Painlevé equation to be found in the literature. Here we return to this problem informed by the subsequent discovery of a Bäcklund transformation for Painlevé II. This enables us to construct exact representations for the electric field and ion distributions for boundary value problems wherein the ratio of fluxes of the positive and negative ions at the boundary adopts one of an infinite sequence of values.

History

Publication title

Journal of Mathematical Analysis and Applications

Volume

240

Pagination

367-381

ISSN

0022-247X

Department/School

School of Natural Sciences

Publisher

Academic Press Inc Elsevier Science

Place of publication

525 B St, Ste 1900, San Diego, USA, Ca, 92101-4495

Rights statement

Copyright 1999 Academic Press

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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