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arXiv · 2405.11763

On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule

Scipio Cuccagna·Masaya Maeda
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Abstract

Assuming as hypotheses the results proved numerically by Chang et al. \cite{Chang} for the exponent $p\in (3,5)$, we prove that some of the ground states of the nonlinear Schrödinger equation (NLS) with pure power nonlinearity of exponent $p$ in the line are asymptotically stable for a certain set of values of the exponent $p$ where the FGR occurs by means of a discrete mode 3rd or 4th order power interaction with the continuous mode. For the 3rd the result is true for generic $p$ while for the 4th order case we assume that there are $p$'s satisfying Fermi Golden rule and the non-resonance condition of the threshold of the continuous spectrum of the linearization. The argument is similar to our recent result valid for $p$ near 3 contained in \cite{CM24D1}.

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Scipio Cuccagna, Masaya Maeda. 2025-04-09. On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule. https://arxiv.org/abs/2405.11763

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