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Gap estimates of the spectrum of the Zakharov-Shabat system. (English) Zbl 0940.35186
Summary: We prove new gap estimates for the Zakharov-Shabat systems with complex periodic potentials. Our method allows us to characterize in a precise way the decreasing properties of the gap length sequence in terms of the regularity of complex potentials in weighted Sobolev spaces.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
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