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| Titel |
Numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation |
| VerfasserIn |
A. Calini, C. M. Schober |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1561-8633
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| Digitales Dokument |
URL |
| Erschienen |
In: Natural Hazards and Earth System Sciences ; 14, no. 6 ; Nr. 14, no. 6 (2014-06-06), S.1431-1440 |
| Datensatznummer |
250118493
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| Publikation (Nr.) |
 copernicus.org/nhess-14-1431-2014.pdf |
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| Zusammenfassung |
| In this article we conduct a broad numerical investigation of stability of
breather-type solutions of the nonlinear Schrödinger (NLS) equation, a
widely used model of rogue wave generation and dynamics in deep water. NLS
breathers rising over an unstable background state are frequently used to
model rogue waves. However, the issue of whether these solutions are robust
with respect to the kind of random perturbations occurring in physical
settings and laboratory experiments has just recently begun to be addressed.
Numerical experiments for spatially periodic breathers with one or two modes
involving large ensembles of perturbed initial data for six typical random
perturbations suggest interesting conclusions. Breathers over an unstable
background with N unstable modes are generally unstable to small
perturbations in the initial data unless they are "maximal breathers"
(i.e., they have N spatial modes). Additionally, among the maximal
breathers with two spatial modes, the one of highest amplitude due to
coalescence of the modes appears to be the most robust. The numerical
observations support and extend to more realistic settings the results of our
previous stability analysis, which we hope will provide a useful tool for
identifying physically realizable wave forms in experimental and
observational studies of rogue waves. |
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