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

Source: [Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint Zakharov-Shabat operator](<https://www.sota2.com/research/paper/68fa545c1e209131ce98aef4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T12:57:32.508Z

Authors: K. Hirota

Published: 2017-04-11T05:00:14.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1704.03145>)

[PDF](<https://arxiv.org/pdf/1704.03145.pdf>)