On the theory of recursion operator
type: Item
instance of: scholarly article
title: On the theory of recursion operator
zbMATH Open document ID: 0594.35080
DOI: 10.1007/BF01403883
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: The recursion operator plays a central role in the theory of nonlinear equations integrable by the inverse scattering method. It generates a whole family of equations integrable by a given spectral problem, starting from a given one. For example, for the famous KdV equation this family is given by (KdV equation corresponds to \(n=1)\) \[ \partial_ tu+\partial_ xL^ nu=0;\quad L=\partial^ 2_ x+2u+2\partial_ x^{-1}\cup \partial,\quad n=1,2,3,.... \] The recursion operator also plays a central role in the Hamilton formulation of the theory of integrable equations. The paper under review contains significant results concerning the theory of the recursion operator associated to Hamiltonian equations. In particular a method of writing down the recursion operator for nonlinear waves in arbitrary dimensions is proposed.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 3955578
zbMATH Keywords: recursion operator
zbMATH Keywords: inverse scattering method
zbMATH Keywords: spectral problem
zbMATH Keywords: Hamiltonian equations
zbMATH Keywords: nonlinear waves
author: V. E. Zakharov
author: B. Konopelchenko
reviewed by: Gheorghe Nenciu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01403883
OpenAlex ID: W2027206921
description: scientific article; zbMATH DE number 3955578