The Hamilton-Jacobi method in the non-Hamiltonian situation and the hydrodynamic substitution
type: Item
instance of: scholarly article
title: The Hamilton-Jacobi method in the non-Hamiltonian situation and the hydrodynamic substitution
zbMATH Open document ID: 1326.34066
DOI: 10.1134/S1064562415020131
author: V. V. Vedenyapin
author: N. N. Fimin
published in: Doklady Mathematics
publication date: 2015-08-21T00:00:00Z
review text: The paper is written using the conventional notation of Hamiltonian dynamics. Through a hydrodynamic substitution (transformation) the authors are able to extend the analysis and solution of the ``Lamb equation'' as developed by Kozlov. For the case of only two dependent variables, the authors are able to obtain solutions via separation of variables. In spite of the theoretical nature of the paper, three illustrative examples are presented. Although brief, the paper is carefully written and self contained. Due to the somewhat specialized subject matter the paper is most likely to be of interest and use to theoreticians and numerical analysts working with Hamilton-Jacobi methods. Some open questions remain as stated in the paper.
reviewed by: Ronald L. Huston
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 82C05
zbMATH DE Number: 6474450
zbMATH Keywords: nonlinear ordinary differential equation systems
zbMATH Keywords: Hamilton systems
zbMATH Keywords: transformations for solutions
MaRDI profile type: Publication
cites work: Q3021449
cites work: Q3345936
cites work: Q4386567
cites work: Q4935264
cites work: The Liouville equation, the hydrodynamic substitution, and the Hamilton-Jacobi equation
cites work: On the topology of steady-state solutions of hydrodynamic and vortex consequences of the Vlasov equation and the Hamilton-Jacobi method
cites work: Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
full work available at URL: s1064562415020131
OpenAlex ID: W797375375
description: scientific article; zbMATH DE number 6474450