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• W3105648412 startingPage "211" @default.
• W3105648412 abstract "The focusing Nonlinear Schrodinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, and MI is considered the main physical mechanism for the appearence of anomalous (rogue) waves (AWs) in nature. In this paper we study, using the finite gap method, the NLS Cauchy problem for generic periodic initial perturbations of the unstable background solution of NLS (what we call the Cauchy problem of the AWs), in the case of a finite number $N$ of unstable modes. We show how the finite gap method adapts to this specific Cauchy problem through three basic simplifications, allowing one to construct the solution, at the leading and relevant order, in terms of elementary functions of the initial data. More precisely, we show that, at the leading order, i) the initial data generate a partition of the time axis into a sequence of finite intervals, ii) in each interval $I$ of the partition, only a subset of ${cal N}(I)le N$ unstable modes are visible, and iii) the NLS solution is approximated, for $tin I$, by the ${cal N}(I)$-soliton solution of Akhmediev type, describing the nonlinear interaction of these visible unstable modes, whose parameters are expressed in terms of the initial data through elementary functions. This result explains the relevance of the $m$-soliton solutions of Akhmediev type, with $mle N$, in the generic periodic Cauchy problem of the AWs, in the case of a finite number $N$ of unstable modes." @default.
• W3105648412 created "2020-11-23" @default.
• W3105648412 creator A5046684160 @default.
• W3105648412 creator A5066352688 @default.
• W3105648412 date "2019-04-01" @default.
• W3105648412 modified "2023-09-26" @default.
• W3105648412 title "The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes" @default.
• W3105648412 cites W121027315 @default.
• W3105648412 cites W1509337642 @default.
• W3105648412 cites W1540991653 @default.
• W3105648412 cites W1545160759 @default.
• W3105648412 cites W1552346269 @default.
• W3105648412 cites W1556972551 @default.
• W3105648412 cites W1631114555 @default.
• W3105648412 cites W1660670830 @default.
• W3105648412 cites W1662771974 @default.
• W3105648412 cites W1966395366 @default.
• W3105648412 cites W1971067396 @default.
• W3105648412 cites W1972140872 @default.
• W3105648412 cites W1972267628 @default.
• W3105648412 cites W1973107894 @default.
• W3105648412 cites W1980663754 @default.
• W3105648412 cites W1989760690 @default.
• W3105648412 cites W1991050432 @default.
• W3105648412 cites W1993166851 @default.
• W3105648412 cites W1996983155 @default.
• W3105648412 cites W1998090080 @default.
• W3105648412 cites W1998285863 @default.
• W3105648412 cites W1998821676 @default.
• W3105648412 cites W2004309739 @default.
• W3105648412 cites W2004706791 @default.
• W3105648412 cites W2009868912 @default.
• W3105648412 cites W2011435718 @default.
• W3105648412 cites W2014386722 @default.
• W3105648412 cites W2014646592 @default.
• W3105648412 cites W2014955706 @default.
• W3105648412 cites W2015970194 @default.
• W3105648412 cites W2022443517 @default.
• W3105648412 cites W2025354537 @default.
• W3105648412 cites W2025603754 @default.
• W3105648412 cites W2028777092 @default.
• W3105648412 cites W2029794467 @default.
• W3105648412 cites W2032514295 @default.
• W3105648412 cites W2032613642 @default.
• W3105648412 cites W2037190242 @default.
• W3105648412 cites W2037553938 @default.
• W3105648412 cites W2039367707 @default.
• W3105648412 cites W2044503648 @default.
• W3105648412 cites W2045416855 @default.
• W3105648412 cites W2049604103 @default.
• W3105648412 cites W2049915610 @default.
• W3105648412 cites W2051694931 @default.
• W3105648412 cites W2058385818 @default.
• W3105648412 cites W2059318397 @default.
• W3105648412 cites W2063739713 @default.
• W3105648412 cites W2069124050 @default.
• W3105648412 cites W2069554118 @default.
• W3105648412 cites W2074044002 @default.
• W3105648412 cites W2078326212 @default.
• W3105648412 cites W2079967947 @default.
• W3105648412 cites W2084424858 @default.
• W3105648412 cites W2090885565 @default.
• W3105648412 cites W2093274602 @default.
• W3105648412 cites W2096569922 @default.
• W3105648412 cites W2102582588 @default.
• W3105648412 cites W2114130739 @default.
• W3105648412 cites W2118575947 @default.
• W3105648412 cites W2140334330 @default.
• W3105648412 cites W2141237926 @default.
• W3105648412 cites W2158066165 @default.
• W3105648412 cites W2161819072 @default.
• W3105648412 cites W2163618760 @default.
• W3105648412 cites W2279352150 @default.
• W3105648412 cites W2288506032 @default.
• W3105648412 cites W2314520473 @default.
• W3105648412 cites W2315382403 @default.
• W3105648412 cites W2332988164 @default.
• W3105648412 cites W2389247390 @default.
• W3105648412 cites W2522501731 @default.
• W3105648412 cites W2531289303 @default.
• W3105648412 cites W2565358629 @default.
• W3105648412 cites W2739195286 @default.
• W3105648412 cites W2741097192 @default.
• W3105648412 cites W2750263077 @default.
• W3105648412 cites W2753507233 @default.
• W3105648412 cites W2794915805 @default.
• W3105648412 cites W2795898826 @default.
• W3105648412 cites W2803747241 @default.
• W3105648412 cites W2889321801 @default.
• W3105648412 cites W2896106153 @default.
• W3105648412 cites W2897627058 @default.
• W3105648412 cites W2898820416 @default.
• W3105648412 cites W2963171244 @default.
• W3105648412 cites W2963735071 @default.
• W3105648412 cites W3021087638 @default.
• W3105648412 cites W3098191389 @default.
• W3105648412 cites W3099836356 @default.
• W3105648412 cites W3104442218 @default.

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