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arXiv · 1704.03145

Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint Zakharov-Shabat operator

K. Hirota
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Abstract

We study the eigenvalues of the self-adjoint Zakharov-Shabat operator corresponding to the defocusing nonlinear Schrodinger equation in the inverse scattering method. Real eigenvalues exist when the square of the potential has a simple well. We derive two types of quantization condition for the eigenvalues by using the exact WKB method, and show that the eigenvalues stay real for a sufficiently small non-self-adjoint perturbation when the potential has some PT-like symmetry.

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K. Hirota. 2017-04-11. Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint Zakharov-Shabat operator. https://doi.org/10.1063/1.4999668

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