The generalized Kupershmidt deformation for the fifth-order coupled KdV equations hierarchy
type: Item
instance of: scholarly article
title: The generalized Kupershmidt deformation for the fifth-order coupled KdV equations hierarchy
zbMATH Open document ID: 1218.35218
published in: Applied Mathematics and Computation
publication date: 2011-04-19T00:00:00Z
review text: The paper belongs to the category of those aiming to generate new integrable systems from a known one through various deformations. The Kupershmidt deformation is generalized as follows: \[ u_{t_n} = B_1\left({{\delta H_{n+1}}\over{\delta u}}- \sum_1^N{{\delta\lambda_j}\over{\delta u}}\right) ;\;(B_2-\alpha_jB_1) \left({{\delta\lambda_j}\over{\delta u}}\right)=0\;,\;j=1,\ldots,N, \] where \(\delta\lambda_j/\delta u\) is the variational derivative of the eigenvalues of the associated spectral problem and \(B_1\), \(B_2\) are two standard Hamiltonian operators. From here, a kind of Hamiltonian soliton equation hierarchy is obtained, describing a 5th order coupled KdV equation.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 5880212
zbMATH Keywords: Kupershmidt deformation
zbMATH Keywords: fifth-order coupled KdV equation
zbMATH Keywords: soliton hierarchy
author: Fa-Jun Yu
MaRDI profile type: Publication
full work available at URL: j.amc.2011.01.105
OpenAlex ID: W2067159842
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DOI: 10.1016/J.AMC.2011.01.105
description: scientific article; zbMATH DE number 5880212