Abstract

The fifth order Kaup-Kupershmidt equation qt = qxxxxx + 5qqxxx + 25/2qxqxx + 5q2q x 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. © World Scientific Publishing Company.