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Gaps of one dimensional periodic AKNS systems. (English) Zbl 0784.34024

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.

MSC:

34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34A55 Inverse problems involving ordinary differential equations
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