Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity
type: Item
instance of: scholarly article
title: Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity
zbMATH Open document ID: 0951.35125
published in: Advances in Differential Equations
publication date: 2000-08-21T00:00:00Z
review text: It is shown that the Cauchy problem for a certain class of one-dimensional nonlinear Schrödinger equations involving a derivative in the nonlinearity is well-posed in the space \(H^1_2\). The proof is based on the Fourier restriction norm and gauge transformation. After an introduction which states the problem and displays the main result, the author derives various preliminary estimates, and proves then his main result, which is an improvement of known results.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1493601
zbMATH Keywords: Cauchy problem
zbMATH Keywords: nonlinear Schrödinger equations
zbMATH Keywords: derivative in the nonlinearity
author: Hideo Takaoka
reviewed by: Guy Jumarie
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1493601