Equations of the inverse problem Bäcklund transformations, and the theory of connections
type: Item
instance of: scholarly article
title: Equations of the inverse problem Bäcklund transformations, and the theory of connections
zbMATH Open document ID: 0947.58035
DOI: 10.1007/BF02365073
author: A. K. Rybnikov
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-10-20T00:00:00Z
review text: As a first step to a geometrization of the Korteweg-de Vries equation \(u_{t} + 12uu_{x} + u_{xxx}=0\), \textit{H. B. Wahlquist} and \textit{F. B. Estabrook} [J. Math. Phys. 16, No. 1, 1-7 (1975; Zbl 0298.35012)] introduced the so-called pseudopotentials as variables in some special differential forms. Later \textit{R. Hermann} [Phys. Rev. Lett. 36, No. 15, 835-836 (1976)] conjectured that those forms are connection forms in a principal bundle. In this paper the construction of \textit{R. Hermann} is revised in all details and his conjecture is proved.
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58A20
zbMATH DE Number: 1348487
zbMATH Keywords: Bäcklund transformations
zbMATH Keywords: connection forms
zbMATH Keywords: inverse problem
reviewed by: Mihai Anastasiei
MaRDI profile type: Publication
cites work: Differential-geometric structures on manifolds
cites work: Q5824959
cites work: Q5558414
cites work: On the geometry of pseudopotentials of evolution equations
cites work: Q3925229
cites work: Q4183082
cites work: Q5731354
cites work: Prolongation structures of nonlinear evolution equations
description: scientific article; zbMATH DE number 1348487