Stability and instability of standing waves for one dimensional nonlinear Schrödinger equations with double power nonlinearity
type: Item
instance of: scholarly article
title: Stability and instability of standing waves for one dimensional nonlinear Schrödinger equations with double power nonlinearity
zbMATH Open document ID: 0868.35111
author: Masahito Ohta
published in: Kodai Mathematical Journal
publication date: 1995-01-01T00:00:00Z
review text: The author considers the stability and instability of standing waves for the following nonlinear Schrödinger equation \[ iu_t+ u_{xx}+ f(u)=0,\quad t\geq 0,\quad x\in\mathbb{R}, \] where \(f(u)= a|u|^{p-1}u+ b|u|^{q-1}\) with \(a,b\in\mathbb{R}\) and \(1<p<q<\infty\). Basically, the author applies the abstract theory of stability and instability by Grillakis, Shatah and Strauss. The result in the paper is interesting.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 76B25
zbMATH DE Number: 815799
zbMATH Keywords: stability and instability of standing waves
zbMATH Keywords: nonlinear Schrödinger equation
reviewed by: Boling Guo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043354
OpenAlex ID: W1965929809
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DOI: 10.2996/KMJ/1138043354
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description: scientific article; zbMATH DE number 815799