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Invariance of the Kaup-Kupershmidt equation and triangular auto-Bäcklund transformations

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" [{\it J. Math. Phys.} {\bf 46}, 073507, 19 pp., 2005]. 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 multipotentialisation of the Kupershmidt equation.

preprint2012arXivOpen access
Marianna EulerNorbert Euler
math-phmath.MPnlin.SI
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Marianna EulerNorbert Euler

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