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.


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