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 volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. ...
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.
This text deals with mathematical statements of a wide class of problems studied in mechanics. In particular, equations of one-dimensional barotropic ...
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 The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian.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...
When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics an...
The study of asymptotic solutions to nonlinear systems of partial differential equations is a powerful tool in the analysis of such systems and their applications in physics, mechanics, and engineering. In this book, the authors propose a method of asymptotic analysis of solutions, which can be applied in the case of the so-called smoothed shock waves, nonlinear waves which vary fast in a neighborhood of the front and slowly outside of this neighborhood. The proposed method, based on the study of geometric objects associated to the front, can be viewed as a generalization of the geometric...
The study of asymptotic solutions to nonlinear systems of partial differential equations is a powerful tool in the analysis of such systems and their ...
