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• W2950966072 abstract "Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent generalizations of the well-known integrable H'{e}non-Heiles systems. The (time-dependent) Hamiltonians are given by logarithmic derivatives of the tau-functions (inherited from the original PDEs). The ODEs for the similarity solutions also have inherited B{a}cklund transformations, which may be used to generate sequences of rational solutions as well as other special solutions related to the first Painlev'{e} transcendent." @default.
• W2950966072 created "2019-06-27" @default.
• W2950966072 creator A5064714239 @default.
• W2950966072 date "1998-07-01" @default.
• W2950966072 modified "2023-10-14" @default.
• W2950966072 title "Non-autonomous Hénon-Heiles systems" @default.
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• W2950966072 doi "https://doi.org/10.1016/s0167-2789(98)00010-4" @default.
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