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

2024/04/22 by Cuccagna, Scipio, Maeda, Masaya · 1 citation
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.14287

Abstract

For exponents p satisfying 0&lt;|p-3|≪ 1 and only in the context of spatially even solutions we prove that the ground states of the nonlinear Schrödinger 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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