Volume 25, Issue 2, March 2018, Pages 247 - 261
Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation
Authors
Colin Rogersc.rogers@unsw.edu.au, Peter A. ClarksonP.A.Clarkson@kent.ac.uk, 
School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW2052, Australia,c.rogers@unsw.edu.au
School of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, CT2 7FS, UK,P.A.Clarkson@kent.ac.uk
Received 16 September 2017, Accepted 9 December 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2018.1452672How to use a DOI?
- Abstract
A class of symmetry transformations of a type originally introduced in a nonlinear optics context is used here to isolate an integrable Ermakov-Painlevé II reduction of a resonant NLS equation which encapsulates a nonlinear system in cold plasma physics descriptive of the uni-axial propagation of magneto-acoustic waves. A Bäcklund transformation is employed in the iterative generation of novel classes of solutions to the cold plasma system which involve either Yablonski-Vorob’ev polynomials or classical Airy functions.
- Copyright
- © 2018 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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TY - JOUR AU - Colin Rogers AU - Peter A. Clarkson PY - 2021 DA - 2021/01/06 TI - Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation JO - Journal of Nonlinear Mathematical Physics SP - 247 EP - 261 VL - 25 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2018.1452672 DO - 10.1080/14029251.2018.1452672 ID - Rogers2021 ER -