The asymptotic stability on the line of ground states of the pure power NLS with $0<|p-3|\ll 1$

Scipio Cuccagna; Masaya Maeda

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arXiv · 2404.14287

The asymptotic stability on the line of ground states of the pure power NLS with $0<|p-3|\ll 1$

Scipio Cuccagna·Masaya Maeda

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Abstract

For exponents $p$ satisfying $0<|p-3|\ll 1$ and only in the context of spatially even solutions we prove that the ground states of the nonlinear Schr\"odinger equation (NLS) with pure power nonlinearity of exponent $p$ in the line are asymptotically stable. The proof is similar to a related result of Martel, preprint arXiv:2312.11016, for a cubic quintic NLS. Here we modify the second part of Martel's argument, replacing the second virial inequality for a transformed problem with a smoothing estimate on the initial problem, appropriately tamed by multiplying the initial variables and equations by a cutoff.

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Scipio Cuccagna, Masaya Maeda. 2024-04-22. The asymptotic stability on the line of ground states of the pure power NLS with $0<|p-3|\ll 1$. https://arxiv.org/abs/2404.14287

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