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A. Osborne (2010)
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B. Zhai, Wei-guo Zhang, Xiaoli Wang, Hai-Qiang Zhang (2013)
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P. Gaillard (2012)
Determinant representation of NLS equation, Ninth Peregrine breather and multi-rogue waves
Kharif Christian, Slunyaev Alexey, Pelinovsky Efim (2009)
Rogue Waves in the Ocean
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Eighth Peregrine breather solution of the NLS equation and multi-rogue waves
We introduce a mechanism for generating higher-order rogue waves (HRWs) of the nonlinear Schrödinger (NLS) equation: the progressive fusion and fission of n degenerate breathers associated with a critical eigenvalue λ 0 creates an order- n HRW. By adjusting the relative phase of the breathers in the interacting area, it is possible to obtain different types of HRWs. The value λ 0 is a zero point of an eigenfunction of the Lax pair of the NLS equation and it corresponds to the limit of the period of the breather tending to infinity. By employing this mechanism we prove two conjectures regarding the total number of peaks, as well as a decomposition rule in the circular pattern of an order- n HRW.
Physical Review E – American Physical Society (APS)
Published: May 24, 2013
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