Abstract
Recent investigations, originating in the fundamental work of Kruskal, Zabusky, and Gardner reveal that a large number of equations governing nonlinear wave motion can be put in a Hamiltonian formalism. Many of these equations turn out to be completely integrable. This chapter describes a miniscule generalization of the Hamiltonian formalism and its applications to the KdV equation to the regularized long wave equation (RLW) championed by Benjamin and others. It reviews classical Hamiltonian mechanics is reviewed. The chapter discusses infinite dimensional Hamiltonian systems, where phase space consists of all real valued C∞ functions that are periodic, say with period 1.
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