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arXiv · 2003.02215

Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem

Igor Chekhovskoy·Sergey Medvedev·Irina Vaseva·Egor Sedov·Mikhail Fedoruk
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Abstract

We propose a new method for finding discrete eigenvalues for the direct Zakharov-Shabat problem, based on moving in the complex plane along the argument jumps of the function $a(\zeta)$, the localization of which does not require great accuracy. It allows to find all discrete eigenvalues taking into account their multiplicity faster than matrix methods and contour integrals. The method shows significant advantage over other methods when calculating a large discrete spectrum, both in speed and accuracy.

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Igor Chekhovskoy, Sergey Medvedev, Irina Vaseva, Egor Sedov, Mikhail Fedoruk. 2020-03-04. Introducing phase jump tracking -- a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem. https://doi.org/10.1016/j.cnsns.2021.105718

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