Hamiltonian field theory close to the wave equation: from Fermi-Pasta-Ulam to water waves

Abstract

In the present work we analyse the structure of the Hamiltonian field theory in the neighbourhood of the wave equation $q_{tt}=q_{xx}$. We show that, restricting to ``graded'' polynomial perturbations in $q_x$, $p$ and their space derivatives of higher order, the local field theory is equivalent, in the sense of the Hamiltonian normal form, to that of the Korteweg-de Vries hierarchy of second order. Within this framework, we explain the connection between the theory of water waves and the Fermi-Pasta-Ulam system.

37 pages; published version with minor changes. Added some remarks and a concluding sectios

References in corpus (5)

• Traveling quasi-periodic water waves with constant vorticity
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