This volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. The book is, in fact, an extension and continuation of the authors' works 59], 60], 65]. The basic ideas are summarized in the Introduction. The book consists of two parts. In the first, the theory of the canonical operator is develop- ed, whereas, in the second, many applications of the canonical operator method to concrete problems of mathematical physics are presented. The authors are pleased to express their deep gratitude to S. M....

This text deals with mathematical statements of a wide class of problems studied in mechanics. In particular, equations of one-dimensional barotropic gas, the Cauchy problem, hyperbolic equations, and the theory of elasticity for media with different moduli of elasticity, are studied.

When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry; indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. Its central mathematical idea is to use topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schrodinger...