The smoothness of scattering operators for sinh-Gordon and nonlinear Schrödinger equations
type: Item
instance of: scholarly article
title: The smoothness of scattering operators for sinh-Gordon and nonlinear Schrödinger equations
zbMATH Open document ID: 1025.35015
publication date: 2003-04-23T00:00:00Z
review text: The author proves the existence and the infinite smoothness of the scattering operator for the sinh-Gordon equation \[ u_{tt}-\Delta u +\frac{(e^u-e^{-u})}{2}=0. \] More precisely, one proves that for \(n\geq 3\), \(s\geq n/2\) there exists \(d>0\) such that the scattering operator carries the set \(\{(\varphi, \psi)\in H^s\times H^{s-1} \mid \|\varphi\|_{H^n/2}+ \|\psi\|_{H^{n/2-1}}\leq \delta\}\) into \(H^s\times H^{s-1}\). The proof is based on some nonlinear estimates in Besov spaces. It is also stated that a similar result holds for the nonlinear Schrödinger equation \[ i u_t+\Delta u +\mu (e^{\lambda |u|^2}-1)u=0. \]
reviewed by: Mihai Pascu
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 1885855
zbMATH Keywords: sinh-Gordon equation
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: scattering operator
author: Baoxiang Wang
MaRDI profile type: Publication
full work available at URL: s10114-002-0193-7
OpenAlex ID: W2004775827
DOI: 10.1007/S10114-002-0193-7
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1885855