ABSTRACT
One of the early successes of Hamiltonian-based stability theory was Benjamin’s (1972) (with mathematical corrections by Bona, 1975) proof of the nonlinear stability of the soliton solution to the Korteweg-de Vries or, more simply, the KdV equation. In this chapter we will describe the Hamiltonian structure of the KdV equation and present the stability theory as a consequence of the underlying Hamiltonian formalism.
