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Generating mechanism for higher-order rogue waves

Generating mechanism for higher-order 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

Generating mechanism for higher-order rogue waves

Physical Review E , Volume 87 (5) – May 24, 2013
10 pages

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References (9)

Publisher
American Physical Society (APS)
Copyright
©2013 American Physical Society
ISSN
1539-3755
DOI
10.1103/PhysRevE.87.052914
pmid
23767605
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Physical Review EAmerican Physical Society (APS)

Published: May 24, 2013

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