Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1997-03-12
Nonlinear Sciences
Exactly Solvable and Integrable Systems
25 pages, Latex. Some minor corrections
Scientific paper
10.1016/S0167-2789(98)00010-4
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.
No associations
LandOfFree
Non-autonomous Hénon-Heiles Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Non-autonomous Hénon-Heiles Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-autonomous Hénon-Heiles Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-436534