Basic Methods of Soliton Theory

The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.

Differential algebra (local conservation laws, Bäcklund–Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann–Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin–Gordon, and Nonlinear Schrödinger equation.