NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan 
blocks

Chvartatskyi, Oleksandr; Müller-Hoissen, Folkert

doi:10.1088/1751-8121/aa6185

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NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks

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Chvartatskyi, Oleksandr
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Müller-Hoissen, Folkert
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Chvartatskyi, O., & Müller-Hoissen, F. (2017). NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks. Journal of Physics A: Mathematical and Theoretical, 50(15): 155204. doi:10.1088/1751-8121/aa6185.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002C-C2C4-8

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.