An algebraic characterization of the Korteweg-de Vries hierarchy
type: Item
instance of: scholarly article
title: An algebraic characterization of the Korteweg-de Vries hierarchy
zbMATH Open document ID: 1028.37040
DOI: 10.1215/S0012-7094-01-10823-5
published in: Duke Mathematical Journal
publication date: 2002-10-27T00:00:00Z
review text: The paper aims to explore the algebraic characteristic property of the Korteweg-de Vries hierarchy. It is shown that the conserved differential polynomials of the Korteweg-de Vries equation \[ u_t=u_{xxx}-12uu_x \] are those with vanishing residues evaluated on the formal power series of the kind \[ u=x^{-2}+u_0+\sum_{n\geq 2}u_nx^n. \] The result reflects the enigmatical university that distinguishes the Sato bilinear identity in soliton theory.
reviewed by: Wen-Xiu Ma
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1820821
zbMATH Keywords: conserved differential polynomial
zbMATH Keywords: KdV hierarchy
author: François Treves
MaRDI profile type: Publication
cites work: Darboux coverings and rational reductions of the KP hierarchy
cites work: Korteweg-deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws
cites work: Integrals of nonlinear equations of evolution and solitary waves
cites work: Q3933364
cites work: A simple model of the integrable Hamiltonian equation
cites work: Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
cites work: Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
cites work: The two-singular-manifold method: I. Modified Korteweg-de Vries and sine-Gordon equations
cites work: Q3715336
cites work: The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
full work available at URL: s0012-7094-01-10823-5
OpenAlex ID: W2086331860
description: scientific article; zbMATH DE number 1820821