Journal
JOURNAL OF OPTICS
Volume 15, Issue 10, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/2040-8978/15/10/105201
Keywords
extreme waves; nonlinear Schrodinger equation; stability of multi-mode breathers
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Funding
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1108973] Funding Source: National Science Foundation
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In physical regimes described by the cubic, focusing, nonlinear Schrodinger (NLS) equation, the N-dimensional homoclinic orbits of a constant amplitude wave with N unstable modes appear to be good candidates for experimentally observable and reproducible rogue waves. These homoclinic solutions include the Akhmediev breathers (N = 1), which are among the most widely adopted spatially periodic models of rogue waves, and their multi-mode generalizations (N > 1), and will be referred to as multi-mode breathers. Numerical simulations and a linear stability analysis indicate that the breathers with a maximal number of modes (maximal breathers) are robust with respect to rather general perturbations of the initial data in a neighborhood of the unstable background.
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