Matches in SemOpenAlex for { <https://semopenalex.org/work/W2962783294> ?p ?o ?g. }
- W2962783294 endingPage "5308" @default.
- W2962783294 startingPage "5258" @default.
- W2962783294 abstract "The focusing nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media; MI is considered the main physical mechanism for the appearance of rogue (anomalous) waves (RWs) in nature. In this paper we study, using the finite gap method, the NLS Cauchy problem for periodic initial perturbations of the unstable background solution of NLS exciting just one of the unstable modes. We distinguish two cases. In the case in which only the corresponding unstable gap is theoretically open, the solution describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and the nonlinear RW stages are described by the 1-breather Akhmediev solution, whose parameters, different at each RW appearence, are always given in terms of the initial data through elementary functions. If the number of unstable modes is >1, this uniform in t dynamics is sensibly affected by perturbations due to numerics and/or real experiments, provoking corrections to the result. In the second case in which more than one unstable gap is open, a detailed investigation of all these gaps is necessary to get a uniform in t dynamics, and this study is postponed to a subsequent paper. It is however possible to obtain the elementary description of the first nonlinear stage of MI, given again by the Akhmediev 1-breather solution, and how perturbations due to numerics and/or real experiments can affect this result. Since the solution of the Cauchy problem is given in terms of different elementary functions in different time intervals, obviously matching in the corresponding overlapping regions, an alternative approach, based on matched asymptotic expansions, is suggested and presented in a separate paper." @default.
- W2962783294 created "2019-07-30" @default.
- W2962783294 creator A5046684160 @default.
- W2962783294 creator A5066352688 @default.
- W2962783294 date "2018-10-18" @default.
- W2962783294 modified "2023-09-30" @default.
- W2962783294 title "The finite gap method and the analytic description of the exact rogue wave recurrence in the periodic NLS Cauchy problem. 1" @default.
- W2962783294 cites W1509337642 @default.
- W2962783294 cites W1545160759 @default.
- W2962783294 cites W1552346269 @default.
- W2962783294 cites W1662771974 @default.
- W2962783294 cites W1700452290 @default.
- W2962783294 cites W1971067396 @default.
- W2962783294 cites W1972140872 @default.
- W2962783294 cites W1972267628 @default.
- W2962783294 cites W1973107894 @default.
- W2962783294 cites W1980278945 @default.
- W2962783294 cites W1980663754 @default.
- W2962783294 cites W1981683093 @default.
- W2962783294 cites W1993166851 @default.
- W2962783294 cites W1996983155 @default.
- W2962783294 cites W1998090080 @default.
- W2962783294 cites W1998285863 @default.
- W2962783294 cites W2004309739 @default.
- W2962783294 cites W2008380185 @default.
- W2962783294 cites W2009868912 @default.
- W2962783294 cites W2011435718 @default.
- W2962783294 cites W2014386722 @default.
- W2962783294 cites W2015970194 @default.
- W2962783294 cites W2022443517 @default.
- W2962783294 cites W2025603754 @default.
- W2962783294 cites W2028777092 @default.
- W2962783294 cites W2029794467 @default.
- W2962783294 cites W2032514295 @default.
- W2962783294 cites W2032613642 @default.
- W2962783294 cites W2034645524 @default.
- W2962783294 cites W2049604103 @default.
- W2962783294 cites W2049915610 @default.
- W2962783294 cites W2051694931 @default.
- W2962783294 cites W2058385818 @default.
- W2962783294 cites W2059318397 @default.
- W2962783294 cites W2063739713 @default.
- W2962783294 cites W2074044002 @default.
- W2962783294 cites W2078326212 @default.
- W2962783294 cites W2079967947 @default.
- W2962783294 cites W2084424858 @default.
- W2962783294 cites W2090885565 @default.
- W2962783294 cites W2093274602 @default.
- W2962783294 cites W2096569922 @default.
- W2962783294 cites W2102582588 @default.
- W2962783294 cites W2114130739 @default.
- W2962783294 cites W2140334330 @default.
- W2962783294 cites W2141237926 @default.
- W2962783294 cites W2158066165 @default.
- W2962783294 cites W2161819072 @default.
- W2962783294 cites W2163618760 @default.
- W2962783294 cites W2288506032 @default.
- W2962783294 cites W2522501731 @default.
- W2962783294 cites W2565358629 @default.
- W2962783294 cites W2739195286 @default.
- W2962783294 cites W2750263077 @default.
- W2962783294 cites W2963171244 @default.
- W2962783294 cites W3098191389 @default.
- W2962783294 cites W3099836356 @default.
- W2962783294 cites W3106084668 @default.
- W2962783294 cites W4211028935 @default.
- W2962783294 cites W595846807 @default.
- W2962783294 doi "https://doi.org/10.1088/1361-6544/aaddcf" @default.
- W2962783294 hasPublicationYear "2018" @default.
- W2962783294 type Work @default.
- W2962783294 sameAs 2962783294 @default.
- W2962783294 citedByCount "48" @default.
- W2962783294 countsByYear W29627832942017 @default.
- W2962783294 countsByYear W29627832942018 @default.
- W2962783294 countsByYear W29627832942019 @default.
- W2962783294 countsByYear W29627832942020 @default.
- W2962783294 countsByYear W29627832942021 @default.
- W2962783294 countsByYear W29627832942022 @default.
- W2962783294 countsByYear W29627832942023 @default.
- W2962783294 crossrefType "journal-article" @default.
- W2962783294 hasAuthorship W2962783294A5046684160 @default.
- W2962783294 hasAuthorship W2962783294A5066352688 @default.
- W2962783294 hasBestOaLocation W29627832942 @default.
- W2962783294 hasConcept C121332964 @default.
- W2962783294 hasConcept C134306372 @default.
- W2962783294 hasConcept C153635880 @default.
- W2962783294 hasConcept C158622935 @default.
- W2962783294 hasConcept C207821765 @default.
- W2962783294 hasConcept C26955809 @default.
- W2962783294 hasConcept C33923547 @default.
- W2962783294 hasConcept C49344536 @default.
- W2962783294 hasConcept C62520636 @default.
- W2962783294 hasConcept C74455749 @default.
- W2962783294 hasConceptScore W2962783294C121332964 @default.
- W2962783294 hasConceptScore W2962783294C134306372 @default.
- W2962783294 hasConceptScore W2962783294C153635880 @default.
- W2962783294 hasConceptScore W2962783294C158622935 @default.
- W2962783294 hasConceptScore W2962783294C207821765 @default.