NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks
arXiv:1609.03391 · doi:10.1088/1751-8121/aa6185
Abstract
The infinite families of Peregrine, Akhmediev and Kuznetsov-Ma breather solutions of the focusing Nonlinear Schroedinger (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.
arXiv comment18 pages, 5 figures, second and third version: Remark 2.3 added, some minor corrections. To appear in J. Phys. A: Math. Theor
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