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| For a third order equation involving two parameters, first introduced by Rosenau and Hyman, all cases admitting fifth order symmetries are identified. Bi-Hamiltonian structures of five less studied cases are established through their invertible links with some famous integrable equations. Therefore, all cases, having fifth order symmetries, of Rosenau and Hyman's equation are integrable in the bi-Hamiltonian sense. As an interesting observation, their Hamiltonian operators are linearly combinations of basic ingredients in the bi-Hamiltonian theory of Korteweg-de Vries and modified Korteweg-de Vries equations. |
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| Keywords:Symmetries, Bi-Hamiltonian structures, Reciprocal transformations |
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