Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation
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Akhmediev, Nail; Ankiewicz, Adrian
Description
We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of...[Show more]
dc.contributor.author | Akhmediev, Nail | |
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dc.contributor.author | Ankiewicz, Adrian | |
dc.date.accessioned | 2015-09-16T05:03:11Z | |
dc.date.available | 2015-09-16T05:03:11Z | |
dc.identifier.issn | 1539-3755 | |
dc.identifier.uri | http://hdl.handle.net/1885/15439 | |
dc.description.abstract | We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave. | |
dc.description.sponsorship | The authors acknowledge the support of the A.R.C. (Discovery Project DP110102068). One of the authors (N.A.) is a grateful recipient of support from the Alexander von Humboldt Foundation (Germany). | |
dc.format | 10 pages | |
dc.publisher | American Physical Society | |
dc.rights | © 2011 American Physical Society. http://www.sherpa.ac.uk/romeo/issn/1539-3755/..."Publisher's version/PDF may be used. On author's personal website, employer's website or institutional repository" from SHERPA/RoMEO site (as at 16/09/15). | |
dc.source | Physical Review E | |
dc.title | Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation | |
dc.type | Journal article | |
local.identifier.citationvolume | 83 | |
dc.date.issued | 2011-04-20 | |
local.publisher.url | http://www.aps.org/ | |
local.type.status | Published Version | |
local.contributor.affiliation | Akhmediev, N., Optical Sciences Group, Research School of Physics and Engineering, The Australian National University | |
local.contributor.affiliation | Ankiewicz, A., Optical Sciences Group, Research School of Physics and Engineering, The Australian National University | |
dc.relation | http://purl.org/au-research/grants/arc/DP110102068 | |
local.bibliographicCitation.issue | 4 | |
local.bibliographicCitation.startpage | 046603 | |
local.identifier.doi | 10.1103/PhysRevE.83.046603 | |
Collections | ANU Research Publications |
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