Non-autonomous Hénon-Heiles systems

✍ Scribed by Andrew N.W. Hone

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 836 KB
• Volume: 118
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(98)00010-4

✦ Synopsis

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 Hrnon-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/icklund transformations, which may be used to generate sequences of rational solutions as well as other special solutions related to the first Painlev~ transcendent.