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 ... » 

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. The analysis of the inverse scattering problem is based on the Riemann problem; GelfandLevitan-Marchenko equations are also treated. The non-linear Schrödinger equation, the sine-Gordon equation, the Heisenberg magnet equation and the Toda lattice are discussed. A natural classification of integrable systems based on Liealgebraic methods is given. «