The inverse scattering transformation and the theory of solitons

The method of inverse scattering transformation and the theory of solitons are among the most recent and fascinating achievements in the domain of applied mathematics. The authors provide an introduction for the uninitiated reader, for the mathematician or physicist who has never heard about solitons, or witnessed only from some distance the excitement that they have created. They present the theory in a mathematically satisfactory and rigorous way. The organization of the book follows essentially the historical line of the development of the method of inverse scattering transformation. An extensive and selfcontained treatment of the direct and the inverse scattering problems for the Schroedinger equation and the generalized Zakharov-Shabat system is given. In the last chapter (devoted to perturbations) one of the frontiers of the theory is presented, where the analysis is still largely in the heuristic stage, and where numerous questions are open. (Auth.)