Abstract
The fifth order Kaup–Kupershmidt equation [Formula: see text] is a most important example of an integrable partial differential equation. Among other properties, it is integrable via scattering/inverse scattering techniques, it admits a bi-Hamiltonian formulation, and it possesses an infinite number of generalized symmetries. In sharp contrast with other integrable equations, however, it has proven very difficult to exhibit explicit solutions to Kaup–Kupershmidt. In this paper, we present several interesting particular solutions to this equation obtained with the help of nonlocal symmetries.
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