Time decay for nonlinear dissipative Schrödinger equations in optical fields
type: Item
instance of: scholarly article
title: Time decay for nonlinear dissipative Schrödinger equations in optical fields
zbMATH Open document ID: 1403.35046
DOI: 10.1155/2016/3702738
author: Nakao Hayashi
author: Pavel I. Naumkin
author: Chunhua Li
published in: Advances in Mathematical Physics
publication date: 2018-10-17T00:00:00Z
review text: Summary: We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearity \(\lambda \left|u\right|^{p - 1} u\) of order \(p \left(n\right) < p \leq 1 + 2 / n\) for arbitrarily large initial data, where the lower bound \(p \left(n\right)\) is a positive root of \(\left(n + 2\right) p^2 - 6 p - n = 0\) for \(n \geq 2\) and \(p \left(1\right) = 1 + \sqrt{2}\) for \(n = 1 \). Our purpose is to extend the previous results for higher space dimensions concerning \(\mathbf{L}^2\)-time decay and to improve the lower bound of \(p\) under the same dissipative condition on \(\lambda \in \mathbb{C}\): \(\operatorname{Im} \; \lambda < 0\) and \(\left|\operatorname{Im} \; \lambda\right| > \left(\left(p - 1\right) / 2 \sqrt{p}\right) \left|\operatorname{R} \operatorname{e} \; \lambda\right|\) as in the previous works.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35Q20
zbMATH DE Number: 6957370
zbMATH Keywords: gauge invariant nonlinearity
Wikidata QID: Q59122232
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3702738
OpenAlex ID: W2254580404
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description: scientific article; zbMATH DE number 6957370