**American Mathematical Society Translations - Series 2**

1993;
256 pp;
Hardcover

MSC: Primary 81; 35;
Secondary 41

Print ISBN: 978-0-8218-7507-0

Product Code: TRANS2/157

List Price: $130.00

AMS Member Price: $104.00

MAA Member Price: $117.00

**Electronic ISBN: 978-1-4704-3368-0
Product Code: TRANS2/157.E**

List Price: $130.00

AMS Member Price: $104.00

MAA Member Price: $117.00

# Wave Propagation. Scattering Theory

Share this page *Edited by *
*M. Sh. Birman*

The papers in this collection were written primarily by members of the St. Petersburg seminar in mathematical physics. The seminar, now run by O. A. Ladyzhenskaya, was initiated in 1947 by V. I. Smirnov, to whose memory this volume is dedicated. The papers in the collection are devoted mainly to wave propagation processes, scattering theory, integrability of nonlinear equations, and related problems of spectral theory of differential and integral operators. The book is of interest to mathematicians working in mathematical physics and differential equations, as well as to physicists studying various wave propagation processes.

#### Readership

Mathematicians working in mathematical physics and differential equations as well as physicists studying various wave propagation processes.

# Table of Contents

## Wave Propagation. Scattering Theory

- Cover Cover11
- Title page v6
- Copyright page vi7
- Contents vii8
- Russian Contents ix10
- Part I. Wave propagation 112
- Perturbation theory for phase integrals and its application to problems of wave propagation 314
- Whitham’s and Fermat’s principles for the problem of evolution of wave beams in a nonlinear inhomogeneous medium 1728
- The splitting of separatrices for a standard family of area-preserving transformations 2738
- Boundary layer of eigenfunctions of a diffusion operator 3748
- Neutron scattering by a point nucleus in a random magnetic field. I 5162
- The splitting of eigenvalues in a double potential well under a partial breaking of symmetry 7990
- Part II. Scattering theory 8596
- A general scheme in the stationary scattering theory 8798
- Coulomb effects in systems of several particles 113124
- On the conditions for existence of wave operators in the nonselfadjoint case 127138
- A crystal model consisting of potentials of zero radius with inner structure 151162
- Part III. Linear differential and pseudodifferential operators 161172
- Representations of 𝐶*-algebras generated by pseudodifferential operators in weighted spaces 163174
- Part IV. Nonlinear equations 189200
- The trace formula for the nonlinear Klein-Gordon equation 191202
- On asymptotics of the solution of the Cauchy problem for the modified Korteweg-de Vries equation 215226
- Symmetric reductions of the Riemann 𝜃-function and some of their applications to the Schrödinger and Boussinesq equations 227238
- Large time asymptotic behavior of solutions of the Cauchy problem for a system of the KdV type with rapidly decaying nonsoliton initial data 239250
- Back Cover Back Cover1271