CV of A.L. Sakhnovich (O. Sakhnovych)

EDUCATION AND SCIENTIFIC CAREER:
Doctor of Sciences (secondary doctorship): Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine.
Date of award: February 1993.
Candidate of Sciences (Ph. D. Math.): Kharkov State University, USSR.
Date of award: May 1982.
M.Sc. Mathematics (distinguished "red" diploma),
Moscow State University, USSR.
Date of award: June 1976.

ACADEMIC AND PROFESSIONAL EXPERIENCE:
2006- till now. Researcher (Senior Postdoc), Faculty of Mathematics, University of Vienna.
1986-2005. Branch of Hydroacoustics, Marine Institute of Hydrophysics, Academy of Sciences of Ukraine
(1993--2005 Senior Scientist).
February 2001--February 2002. Division of Mathematics, School of Technology, University of Glamorgan: Research Fellow, on leave from Branch of Hydroacoustics.
1998-1999. Acting Professor at the Odessa Pedagogical University.
1995-1997, Faculty of Mathematics and Informatics, Amsterdam Free University: Researcher, on leave from Branch of Hydroacoustics.
1976-1986. Odessa Branch, Institute of Economics, Academy of Sciences of Ukraine, Ukraine.

RESEARCH INTERESTS:
1. Inversion, interpolation, and regularization problems.
2. Direct and inverse problems; spectral, scattering, and bispectral theories of the linear differential equations and structured matrices (both self-adjoint and non-self-adjoint cases); bound states, explicit, global, and fundamental solutions; Weyl-Titchmarsh functions. The cases of the Dirac-type, canonical, and Sturm-Liouville matrix equations,
in particular.
3. PDE, integrable nonlinear equations: explicit solutions and initial-boundary value problems; slowly decaying solutions, asymtotics, nonsingular solutions and singularities; one and several space variables.
4. Applications to mathematical physics and engineering problems.

METHODS:
The methods of the interpolation, operator, control, and system theories, state space methods are widely used, especially the notion of the transfer matrix-function. An approach to the solution of the self-adjoint and non-self-adjoint inverse problems directly via Weyl functions has been developed. As a result, the open Goursat problem for the second harmonic generation model has been solved. Another series of applications is connected with Borg-Marchenko-type uniqueness theorems. In addition, a version of the Bäcklund-Darboux transformation, where matrices and corresponding "generalized" eigenfunctions are used instead of the traditional eigenvalues and eigenfunctions, has been introduced and various applications were obtained.