Inverse Problems and Nonlinear Evolution Equations ― Solutions, Darbourx Matrices and Weyl-titchmarch Functions

A. Sakhnovich (mathematics, U. of Vienna), L.A. Sakhnovich, and Roitberg (mathematics and computer science, U. Leipzig, Germany) explore the method of operator identities and the related theory of S-nodes, both developed by L.A. Sakhnovich. The notion of the transfer matrix function generated by the S-mode plays an essential role, they say. After preliminaries, they cover self-adjoint and skew-self-adjoint Dirac systems: rectangular matrix potentials, linear system auxiliary to the nonlinear optics equation, discrete systems, integrable nonlinear equations, generalized Backlund-Darboux transformation (GBDT) theorems and explicit solutions of nonlinear equations, some further results on inverse problems and GBDT, and sliding inverse problems for radial Dirac and Schrodinger equations. Some basic knowledge of linear algebra, calculus, and operator theory from standard university courses is required. Annotation c2013 Book News, Inc., Portland, OR (booknews.com)

Alexander L. Sakhnovich, University of Vienna, Austria; Lev A. Sakhnovich, Milford, Connecticut, USA;Inna Ya. Roitberg, Universitat Leipzig, Germany.