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• W2750263077 startingPage "973" @default.
• W2750263077 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, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the x-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of N=1,2 unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearance, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence." @default.
• W2750263077 created "2017-08-31" @default.
• W2750263077 creator A5046684160 @default.
• W2750263077 creator A5066352688 @default.
• W2750263077 date "2018-04-01" @default.
• W2750263077 modified "2023-09-29" @default.
• W2750263077 title "The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes" @default.
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• W2750263077 doi "https://doi.org/10.1016/j.physleta.2018.02.014" @default.
• W2750263077 hasPublicationYear "2018" @default.
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