Hamiltonian Methods in the Theory of Solitons

Presents the foundations of the inverse scattering method and its application to soliton theory. The main emphasis is on Hamiltonian interpretation, based on an elegant and unifying notion of the r-matrix - though analysis of the inverse scattering problem, based on the Riemann problem GelfandLevitan-Marchenko equations, is also treated. Also discussed are the non-linear Schrodinger equation, the sine-Gordon equation, the Heisenberg magnet equation and the Toda lattice. A natural classification of integrable systems based on Liealgebraic methods is also given.