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.