American Mathematical Society TranslationsSeries 2 1993; 256 pp; hardcover Volume: 157 ISBN10: 0821875078 ISBN13: 9780821875070 List Price: US$130 Member Price: US$104 Order Code: TRANS2/157
 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 Part I. Wave propagation  V. S. Buldyrev and N. S. Grigor'eva  Perturbation theory for phase integrals and its application to problems of wave propagation
 S. A. Vakulenko and I. A. Molotkov  Whitham's and Fermat's principles for the problem of evolution of wave beams in a nonlinear inhomogeneous medium
 V. F. Lazutkin  The splitting of separatrices for a standard family of areapreserving transformations
 K. A. Makarov  Boundary layer of eigenfunctions of a diffusion operator
 B. S. Pavlov and A. E. Ryzhkov  Neutron scattering by a point nucleus in a random magnetic field. I
 T. F. Pankratova  The splitting of eigenvalues in a double potential well under a partial breaking of symmetry
Part II. Scattering theory  M. Sh. Birman and D. R. Yafaev  A general scheme in the stationary scattering theory
 A. A. Kvitsinskiĭ, Yu. A. Kuperin, and S. P. Merkur'ev  Coulomb effects in systems of several particles
 S. N. Naboko  On the conditions for existence of wave operators in the nonselfadjoint case
 B. S. Pavlov and N. V. Smirnov  A crystal model consisting of potentials of zero radius with inner structure
Part III. Linear differential and pseudodifferential operators  B. A. Plamenevskiĭ and V. N. Senichkin  Representations of \(C^*\)algebras generated by pseudodifferential operators in weighted spaces
 Part IV. Nonlinear equations
 V. S. Buslaev and E. A. Rybakina  The trace formula for the nonlinear KleinGordon equation
 A. R. Its  On asymptotics of the solution of the Cauchy problem for the modified Kortewegde Vries equation
 V. B. Matveev and A. O. Smirnov  Symmetric reductions of the Riemann \(\theta\)function and some of their applications to the Schrödinger and Boussinesq equations
 V. V. Sukhanov  Large time asymptotic behavior of solutions of the Cauchy problem for a system of the KdV type with rapidly decaying nonsoliton initial data
