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Hardcover ISBN:  9780821875070 
eBook ISBN:  9781470433680 
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Book DetailsAmerican Mathematical Society Translations  Series 2Volume: 157; 1993; 256 ppMSC: Primary 81; 35; Secondary 41
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.
ReadershipMathematicians 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


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

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