Jens Wittsten

I will talk about an eigenvalue problem for a non-self-adjoint semiclassical Zakharov-Shabat operator on the circle. This operator appears in the Lax pair representation when treating the focusing nonlinear Schrödinger equation via the inverse scattering method. In the talk I will describe how the asymptotic distribution of semiclassical eigenvalues can be given in terms of Bohr-Sommerfeld type quantization
conditions. To obtain the quantization conditions we use the exact WKB method, which involves a convergent resummation of the WKB asymptotic expansion in a turning-point-free complex region. The talk is based on joint work with Setsuro Fujiie.