Grébert, Benoît; Guillot, Jean-Claude Gaps of one dimensional periodic AKNS systems. (English) Zbl 0784.34024 Forum Math. 5, No. 5, 459-504 (1993). This paper is devoted to some specific aspects of the inverse periodic problem associated to \(2\times 2\) first order Ablowitz-Kaup-Newell-Segur (AKNS) systems with real-valued periodic potentials. The authors especially study the signed gap length map associated with periodic AKNS systems in a Hilbert space setting. They prove, for example, that the sequence of gap lengths in some sense characterizes the periodic spectrum. Reviewer: B.Hofmann (Chemnitz) Cited in 15 Documents MSC: 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 34A55 Inverse problems involving ordinary differential equations Keywords:inverse periodic problem; first order Ablowitz-Kaup-Newell-Segur (AKNS) systems; periodic potentials; gap length map; periodic spectrum PDFBibTeX XMLCite \textit{B. Grébert} and \textit{J.-C. Guillot}, Forum Math. 5, No. 5, 459--504 (1993; Zbl 0784.34024) Full Text: DOI EuDML