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تسجيل مستخدم جديدA class of stable perturbations for a minimal mass soliton in three dimensional saturated nonlinear Schrodinger equations
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تأليف
Jeremy Marzuola
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In this result, we develop the techniques of cite{KS1} and cite{BW} in order to determine a class of stable perturbations for a minimal mass soliton solution of a saturated, focusing nonlinear Schrodinger equation {c} i u_t + Delta u + beta (|u|^2) u = 0 u(0,x) = u_0 (x), in $reals^3$. By projecting into a subspace of the continuous spectrum of $mathcal{H}$ as in cite{S1}, cite{KS1}, we are able to use a contraction mapping similar to that from cite{BW} in order to show that there exist solutions of the form e^{i lambda_{min} t} (R_{min} + e^{i mathcal{H} t} phi + w(x,t)), where $e^{i mathcal{H} t} phi + w(x,t)$ disperses as $t to infty$. Hence, we have long time persistance of a soliton of minimal mass despite the fact that these solutions are shown to be nonlinearly unstable in cite{CP1}.
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