openAccessArticle: Falsecover date: 2015-12-01pii: S0167-2789(15)00177-3Harvest Date: 2016-01-06 13:08:11issueName:Page Range: 81-81href scidir: http://www.sciencedirect.com/science/article/pii/S0167278915001773pubType

We study the linear stability of the Peregrine breather both numerically and with analytical arguments based on its derivation as the singular limit of a single-mode spatially periodic breather as the spatial period becomes infinite. By constructing solutions of the linearization of the nonlinear Schrödinger equation in terms of quadratic products of components of the eigenfunctions of the Zakharov-Shabat system, we show that the Peregrine breather is linearly unstable. A numerical study employing a highly accurate Chebychev pseudo-spectral integrator confirms exponential growth of random initial perturbations of the Peregrine breather.

Abstract. In this paper we investigate the effects of nonlinear damping with and without linear damping/forcing in a sea state modeled by higher-order NLS in a two unstable mode regime. In particular, we are interested in how the linear term affects downshifting, rogue wave formation, and the number of rogue waves. We find that irreversible downshifting occurs when the nonlinear damping is the dominant damping effect. In particular, when only nonlinear damping is present, permanent downshifting occurs for all values of the nonlinear damping parameter β , appearing abruptly for larger values of β . We find including linear damping weakens the nonlinear damping effect of downshifting while linear forcing enhances the downshifting.

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