Some remarks on a WKB method for the nonselfadjoint Zakharov-Shabat eigenvalue problem with analytic potentials and fast phase. (English) Zbl 1037.81043
Summary: A formal method for approximating eigenvalues of the nonselfadjoint Zakharov-Shabat eigenvalue problem in the semi-classical scaling is described. Analyticity of the potential is assumed and appears to be crucial. The method involves finding appropriate paths between pairs of complex turning points, and reproduces the \(Y\)-shaped spectra observed by J. C. Bronski [Physica D 97, 376–397 (1996)]. An application to all-optical ultrashort pulse generation is briefly described, and the kind of tools that are required to make the results rigorous are indicated.
MSC:
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
References:
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