This collection contains papers by participants in the Seminar on Mathematical Physics in Kharkov, Ukraine. The papers mainly focus on nontraditional problems of spectral theory, such as new types of inverse problems for one-dimensional differential operators, new classes of solutions to nonlinear differential equations obtained using spectral methods, distribution of eigenvalues of large random matrices, and related problems of statistical physics of disordered systems. In addition, the papers explore the spectral aspects of homogenization and of properties of ergodic dynamical systems. All the papers contain original results published for the first time.
Limits of the reflectionless Dirac operator by D. S. Lundina and V. A. Marchenko Quasianalytic classes and isospectral Hill's operators by M. Novitskii Discriminants and generic spectra of nonselfadjoint Hill's operators by V. A. Tkachenko On cocycles of ergodic dynamical systems and automorphisms compatible with them by V. Ya. Golodets, A. I. Danilenko, and S. I. Bezuglyi On the eigenvalue distribution of the deformed Wigner ensemble of random matrices by A. M. Khorunzhy and L. A. Pastur Soliton asymptotics of nondecreasing solutions of nonlinear completely integrable evolution equations by E. Ya. Khruslov and V. P. Kotlyarov The Cauchy problem for the KdV equation with almost periodic initial data whose spectrum is nowhere dense by I. E. Egorova The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and increasing functions by D. G. Shepelsky Homogenization of boundary problems for the Ginzburg-Landau equation in weakly connected domains by E. Khruslov and L. Pankratov The infinite component limit of the random anisotropy $n$-vector model by B. Khoruzhenko, L. Pastur, and M. Shcherbina.