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• W2511452607 abstract "We consider the emph{focusing} nonlinear Schrodinger equation posed on the one dimensional line, with nonzero background condition at spatial infinity, given by a homogeneous plane wave. For this problem of physical interest, we study the initial value problem for perturbations of the background wave in Sobolev spaces. It is well-known that the associated linear dynamics for this problem describes a phenomenon known in the literature as emph{modulational instability}, also recently related to the emergence of emph{rogue waves} in ocean dynamics. In qualitative terms, small perturbations of the background state increase its size exponentially in time. In this paper we show that, even if there is no time decay for the linear dynamics due to the modulationally unstable regime, the equation is still locally well-posed in $H^s$, $s>frac12$. We apply this result to give a rigorous proof of the unstable character of two well-known NLS solutions: the Peregrine and Kuznetsov-Ma breathers." @default.
• W2511452607 created "2016-09-16" @default.
• W2511452607 creator A5006963626 @default.
• W2511452607 date "2016-08-29" @default.
• W2511452607 modified "2023-09-27" @default.
• W2511452607 title "Well-posedness for modulationally unstable nonlinear Schrodinger equations, and applications" @default.
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