Blowup in the nonlinear Schrödinger equation near critical dimension
type: Item
instance of: scholarly article
title: Blowup in the nonlinear Schrödinger equation near critical dimension
zbMATH Open document ID: 1027.35132
author: Vivi Rottschäfer
author: Tasso J. Kaper
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-04T00:00:00Z
review text: This paper deals with the cubic nonlinear Schrödinger equation with initial conditions \(\Phi(x,0)= \Phi_0(x)\), where \(x\in\mathbb{R}^d\) and \(2<d\leq 4\). More precisely, the authors study the case when \(d\) is algebraically close to 2. In particular, they study the values of \(d\) for which \(d-2=a^l\), for every \(l>0\), where \(a\) is a small parameter. The main result is the construction of a locally unique, monotonically decreasing in modulus, self-similar solution connecting 0 to \(\infty\).
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1763473
zbMATH Keywords: critical dimension
zbMATH Keywords: blow-up phenomena
zbMATH Keywords: cubic nonlinear Schrödinger equation
zbMATH Keywords: self-similar solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7814
OpenAlex ID: W2070693549
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DOI: 10.1006/JMAA.2001.7814
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description: scientific article; zbMATH DE number 1763473