The complex WKB method for nonlinear equations I
Subtitle: linear theory
By: Victor P. Maslov ; translated from the Russian by M.A. Shishkova and A.B. Sossinsky
Contributors: Shishkova, M. A.; Sossinsky, A. B.
Series: Progress in physics -- v. 16; Progress in physics (Boston, Mass.) -- v. 16.
Publisher: Springer Basel AG
Published: 1994
Place of publication: Basel
Language: eng
Format: [electronic resource] :
Number of pages: 300
ISBN-13: 9783034885362; 9783034896696
Subjects: Nonlinear Differential equations; Linear Differential equations; Mathematical physics; WKB approximation; Asymptotic theory
Work titles: Kompleksnyĭ metod VKB v nelineĭnykh uravnenii͡akh
Description: 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 The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian.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 Schrödinger equation, and also to take into account the so-called tunnel effects. Finite-dimensional linear theory is reviewed in detail. Infinite-dimensional linear theory and its applications to quantum statistics and quantum field theory, as well as the nonlinear theory (involving instantons), will be considered in a second volume.
Notes: Originally published by Birkhäuser Verlag in 1994.

Softcover reprint of the hardcover 1st edition 1994.

Includes bibliographical references.