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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