Abstract
We consider the restriction of isospectral flows to stationary manifolds. Specifically, we present a systematic construction of Hamiltonian structures written in stationary manifold coordinates, which demonstrates the close relationship between the Hamiltonian formulations of nonlinear evolution equation (PDE) and its stationary reduction. We illustrate these ideas in the context of the KdV and 5th order KdV equations.
We then apply these ideas to the Boussinesq hierarchy, associated with the (trace free) 3rd order Lax operator, together with the Sawada-Kotera and Kaup-Kupershmidt reductions.
We use our results to study the integrable cases of the Hénon Heiles equation.
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Dedicated to the memory of Irina Dorfman
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© 1997 Birkhäuser Boston
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Fordy, A.P., Harris, S.D. (1997). Hamiltonian Structures in Stationary Manifold Coordinates. In: Fokas, A.S., Gelfand, I.M. (eds) Algebraic Aspects of Integrable Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 26. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2434-1_6
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DOI: https://doi.org/10.1007/978-1-4612-2434-1_6
Publisher Name: Birkhäuser Boston
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