NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks
Oleksandr Chvartatskyi, Folkert Müller-Hoissen
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Source: Crossref
Published: Mar 14, 2017
DOI: 10.1088/1751-8121/aa6185
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Abstract The infinite families of Peregrine, Akhmediev and Kuznetsov–Ma breather solutions of the focusing nonlinear Schrödinger (NLS) equation are obtained via a matrix version of the Darboux transformation, with a spectral matrix of the form of a Jordan block. The structure of these solutions is essentially determined by the corresponding solution of the Lyapunov equation. In particular, regularity follows from properties of the Lyapunov equation.
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