Publisher's Synopsis
This volume outlines the basic features of algebraic and spectral methods for nonlinear wave equations, or systems of partial differential equations frequently used in science and engineering. The book covers fundamental materials of the Lie's transformation method, inverse scattering formulation and developments in these and related fields, marked by the discovery of soliton by Zabusky and Kruskal in 1967. The subjects covered are Lie-Backlund symmetries (generalized symmetries), Backlund transformation, recursion operator for the symmetries, Lax representation, variational formalism, analysis of the inverse scattering method, bilinear form method, Riemann-Hilbert problem and the periodic boundary value problem of the inverse scattering method. In the course of the presentation, this volume also introduces the Wahlquist-Estabrook method, Hamiltonian formalism, dressing method by Zakharov-Shabat and a-problem. Some of the topics covered are presented in book form for the first time.;The book is intended for students and specialists in mathematical physics, applied mathematics and related fields. Readers are not required to have the knowledge of more than university mathematics for engineering and physics.
