Invariance of the Kaup-Kupershmidt equation and triangular auto-B\"acklund transformations
Exactly Solvable and Integrable Systems
2012-04-23 v1 Mathematical Physics
math.MP
Abstract
We report triangular auto-B\"acklund 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" [{\it J. Math. Phys.} {\bf 46}, 073507, 19 pp., 2005]. These auto-B\"acklund transformations can then be applied to generate solutions of the Kaup-Kupershmidt equation. We show that triangular auto-B\"acklund transformations result from a systematic multipotentialisation of the Kupershmidt equation.
Keywords
Cite
@article{arxiv.1204.4569,
title = {Invariance of the Kaup-Kupershmidt equation and triangular auto-B\"acklund transformations},
author = {Marianna Euler and Norbert Euler},
journal= {arXiv preprint arXiv:1204.4569},
year = {2012}
}
Comments
Accepted for publication in Journal of Nonlinear Mathematical Physics, Vol. 19