Sakhnovich, Alexander Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation. (English) Zbl 1151.35105 Inverse Probl. 24, No. 2, Article ID 025026, 23 p. (2008). Summary: A Borg-Marchenko-type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the \(N\)-wave equation. A procedure to solve the inverse problem is used for this purpose. The asymptotic condition on the Weyl function, under which the inverse problem is uniquely solvable, is completed by a new and simple sufficient condition on the potential, which implies this asymptotic condition. The evolution of the Weyl function is discussed and the solution of an initial-boundary-value problem for the \(N\)-wave equation follows. Explicit solutions of an inverse problem are obtained. The system with a shifted argument is treated. Cited in 6 Documents MSC: 35R30 Inverse problems for PDEs 35Q60 PDEs in connection with optics and electromagnetic theory 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 78A10 Physical optics Keywords:nonlinear optics equation; Borg-Marchenko theorem; Bäcklund-Darboux transformation; Weyl functions PDFBibTeX XMLCite \textit{A. Sakhnovich}, Inverse Probl. 24, No. 2, Article ID 025026, 23 p. (2008; Zbl 1151.35105) Full Text: DOI arXiv