**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

2003; 284 pp; Hardcover

MSC: Primary 34; 35; 81;

Print ISBN: 978-0-8218-3336-0

Product Code: TRANS2/208

Print ISBN: 978-0-8218-3336-0

Product Code: TRANS2/208

List Price: $135.00

Individual Member Price: $108.00

**Electronic ISBN: 978-1-4704-3419-9
Product Code: TRANS2/208.E**

List Price: $135.00

Individual Member Price: $108.00

# Asymptotic Methods for Wave and Quantum Problems

Share this page *Edited by *
*M. V. Karasev*

The collection consists of four papers in different areas of mathematical
physics united by the intrinsic coherence of the asymptotic methods used. The
papers describe both the known results and most recent achievements, as well as
new concepts and ideas in mathematical analysis of quantum and wave
problems.

In the introductory paper “Quantization and Intrinsic Dynamics”
a relationship between quantization of symplectic manifolds and nonlinear wave
equations is described and discussed from the viewpoint of the weak asymptotics
method (asymptotics in distributions) and the semiclassical approximation
method. It also explains a hidden dynamic geometry that arises when using these
methods.

Three other papers discuss applications of asymptotic methods to the
construction of wave-type solutions of nonlinear PDE's, to the theory of
semiclassical approximation (in particular, the Whitham method) for nonlinear
second-order ordinary differential equations, and to the study of the
Schrödinger type equations whose potential wells are sufficiently shallow
that the discrete spectrum contains precisely one point.

All the papers contain detailed references and are oriented not only to
specialists in asymptotic methods but also to a wider audience of researchers
and graduate students working in partial differential equations and
mathematical physics.

#### Readership

Graduate students and research mathematicians interested in asymptotic methods, partial differential equations, and mathematical physics.

# Table of Contents

## Asymptotic Methods for Wave and Quantum Problems

- Cover Cover11
- Title page iii4
- Copyright page iv5
- Contents v6
- Preface vii8
- Quantization and intrinsic dynamics 110
- Weak asymptotics method and interaction of nonlinear waves 3342
- Global asymptotics and quantization rules for nonlinear differential equations 165174
- Asymptotics of eigenfunctions in shallow potential wells and related problems 235244
- Back Cover Back Cover1296