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.
18 pages, 5 figures, second and third version: Remark 2.3 added, some minor corrections. To appear in J. Phys. A: Math. Theor