Journal of Nonlinear Mathematical Physics

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Volume 19, Issue 3, September 2012, Pages 285 - 291

Invariance of the Kaup–Kupershmidt Equation and Triangular Auto-Bäcklund Transformations

Authors
Marianna Euler*, Norbert Euler†
Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
Received 12 February 2012, Accepted 20 April 2012, Available Online 20 September 2012.
DOI
10.1142/S140292511220001XHow to use a DOI?
Keywords
Integrable evolution equations; auto-Bäcklund transformations; invariance
Abstract

We report triangular auto-Bäcklund transformations for the solutions of a fifth-order evolution equation, which is a constraint for an invariance condition of the Kaup–Kupershmidt equation derived by E. G. Reyes in his paper titled “Nonlocal symmetries and the Kaup–Kupershmidt equation” [J. Math. Phys. 46 (2005) 073507, 19 pp.]. These auto-Bäcklund transformations can then be applied to generate solutions of the Kaup–Kupershmidt equation. We show that triangular auto-Bäcklund transformations result from a systematic multipotentialization of the Kupershmidt equation.

Copyright
© 2012 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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Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
19 - 3
Pages
285 - 291
Publication Date
2012/09/20
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S140292511220001XHow to use a DOI?
Copyright
© 2012 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/).

Cite this article

risenwbib
TY  - JOUR
AU  - Marianna Euler
AU  - Norbert Euler
PY  - 2012
DA  - 2012/09/20
TI  - Invariance of the Kaup–Kupershmidt Equation and Triangular Auto-Bäcklund Transformations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 285
EP  - 291
VL  - 19
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1142/S140292511220001X
DO  - 10.1142/S140292511220001X
ID  - Euler2012
ER  -