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- W2952886458 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.
- W2952886458 created "2019-06-27" @default.
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- W2952886458 date "2016-08-29" @default.
- W2952886458 modified "2023-09-27" @default.
- W2952886458 title "Instability in nonlinear Schrodinger breathers" @default.
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