Geometry of KdV. I: Addition and the unimodular spectral classes
type: Item
instance of: scholarly article
title: Geometry of KdV. I: Addition and the unimodular spectral classes
zbMATH Open document ID: 0651.35074
DOI: 10.4171/RMI/32
published in: Revista Matemática Iberoamericana
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/39327
review text: This is the first of three papers on the geometry of KdV. There is considered a foliation of an extensive function space into which all known invariant manifolds of KdV fit naturally as special leaves. In this paper two main new notions are introduced. The first of them is addition as a generalisation of the Darboux transformation of the Schrödinger operator \(Q=-D\) \(2+q(x)\) with infinitely differentiable real-valued potential vanishing rapidly at \(\pm \infty\) into Q-2D 2 ln \(e_ 1=Q\)-, where \(e_ 1\) is an eigenfunction. The second of them are unimodular spectral classes. The present article investigates the unimodular spectral class with special attention to the invariant \(\sqrt{\det dF(\lambda)}\), where dF(\(\lambda)\) is a (2\(\times 2)\) spectral weight.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 4061806
zbMATH Keywords: eigenfunction
zbMATH Keywords: Hill's operator
zbMATH Keywords: geometry of KdV
zbMATH Keywords: foliation
zbMATH Keywords: extensive function space
zbMATH Keywords: invariant manifolds
zbMATH Keywords: addition
zbMATH Keywords: Darboux transformation
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: unimodular spectral classes
zbMATH Keywords: unimodular spectral class
zbMATH Keywords: spectral weight
author: Henry P. McKean
MaRDI profile type: Publication
OpenAlex ID: W4256729402
description: scientific article; zbMATH DE number 4061806