Advanced Series in Mathematical Physics

"There is a bibliography of 112 items. This book is pedagogically written and is highly recommended for its detailed description of the resolvent method for soliton equations." Mathematical Reviews, 1993 "The book of L A Dickey presents one more point of view on the mathematical theory of solitons or, in other words, on the theory of nonlinear partial differential equations ... The series of joint papers of I M Gelfand and L A Dickey in the middle of the seventies was an important step in the development of the mathematical theory of nonlinear integrable equations ... As a whole the book presents a very good exposition of the important part of the soliton theory." Mathematics Abstracts

• Integrable systems generated by linear differential nth order operators; Hamiltonian structures; Hamiltonian structures of the KdV-hierarchies; the Kupershmidt-Wilson theorem; the KP-hierarchy; Hamiltonian structure of the KP-hierarchy; Baker function, tau-function; Grassmannian, tau-function and Baker function after Segal and Wilson. Algebraic-geometrical Krichever's solutions; matrix first-order operators; KdV-hierarchies as reductions of matrix hierarchies; stationary equations; stationary equations of the KdV-hierarchy in the narrow sense (n=2); stationary equations of the matrix hierarchy; stationary equations of the KdV-hierarchies; matrix differential operators polynomially depending on a parameter; multi-time Lagrangian and Hamiltonian formalism; further examples and applications.